A Library of Distance Distributions of Binary Orthogonal Arrays
This library contains the results from the distance distributions algorithm.
Our research is based on the book Orthogonal Arrays: Theory and Applications[1] by A. Hedayat, N. J. A. Sloane, J. Stufken. The results are tested using the arrays listed in Sloane's Library of Orthogonal Arrays.
For a (n, M, τ) BOA the distance distributions are given as follows:
n.M.τ W = P ∪ Q , (all = internal ∪ external) where
W = P ∪ Q are the reduced distance distributions as described in [4]
all = internal ∪ external are the all possible DDs which are generated as in [2] and [3]
Contents:
Row 8.16.3
7.8.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 8, 2) has 1 (1) possible DDs
- (3, 8, 2) has 3 (3) possible DDs
- (4, 8, 2) has 4 (4) possible DDs
- (5, 8, 2) has 3 (3) possible DDs
- (6, 8, 2) has 3 (5) possible DDs
- (7, 8, 2) has 4 (8) possible DDs
8.16.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 16, 3) has 1 (1) possible DDs
- (4, 16, 3) has 3 (3) possible DDs
- (5, 16, 3) has 4 (4) possible DDs
- (6, 16, 3) has 2 (3) possible DDs
- (7, 16, 3) has 2 (4) possible DDs
- (8, 16, 3) has 3 (7) possible DDs
Row 12.2048.10
4.8.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 8, 2) has 1 (1) possible DDs
- (3, 8, 2) has 3 (3) possible DDs
- (4, 8, 2) has 4 (4) possible DDs
5.16.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 16, 3) has 1 (1) possible DDs
- (4, 16, 3) has 3 (3) possible DDs
- (5, 16, 3) has 4 (4) possible DDs
6.32.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 32, 4) has 1 (1) possible DDs
- (5, 32, 4) has 3 (3) possible DDs
- (6, 32, 4) has 4 (4) possible DDs
7.64.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 64, 5) has 1 (1) possible DDs
- (6, 64, 5) has 3 (3) possible DDs
- (7, 64, 5) has 4 (4) possible DDs
8.128.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 128, 6) has 1 (1) possible DDs
- (7, 128, 6) has 3 (3) possible DDs
- (8, 128, 6) has 4 (4) possible DDs
9.256.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 256, 7) has 1 (1) possible DDs
- (8, 256, 7) has 3 (3) possible DDs
- (9, 256, 7) has 4 (4) possible DDs
10.512.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 512, 8) has 1 (1) possible DDs
- (9, 512, 8) has 3 (3) possible DDs
- (10, 512, 8) has 4 (4) possible DDs
11.1024.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 1024, 9) has 1 (1) possible DDs
- (10, 1024, 9) has 3 (3) possible DDs
- (11, 1024, 9) has 4 (4) possible DDs
12.2048.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 2048, 10) has 1 (1) possible DDs
- (11, 2048, 10) has 3 (3) possible DDs
- (12, 2048, 10) has 4 (4) possible DDs
Row 12.24.3
11.12.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 12, 2) has 1 (1) possible DDs
- (3, 12, 2) has 4 (4) possible DDs
- (4, 12, 2) has 5 (6) possible DDs
- (5, 12, 2) has 10 (12) possible DDs
- (6, 12, 2) has 11 (17) possible DDs
- (7, 12, 2) has 14 (20) possible DDs
- (8, 12, 2) has 18 (29) possible DDs
- (9, 12, 2) has 13 (36) possible DDs
- (10, 12, 2) has 8 (46) possible DDs
- (11, 12, 2) has 8 (58) possible DDs
12.24.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 24, 3) has 1 (1) possible DDs
- (4, 24, 3) has 4 (4) possible DDs
- (5, 24, 3) has 3 (5) possible DDs
- (6, 24, 3) has 6 (9) possible DDs
- (7, 24, 3) has 4 (12) possible DDs
- (8, 24, 3) has 7 (18) possible DDs
- (9, 24, 3) has 7 (22) possible DDs
- (10, 24, 3) has 5 (35) possible DDs
- (11, 24, 3) has 4 (35) possible DDs
- (12, 24, 3) has 5 (50) possible DDs
Row 16.32.3
15.16.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 16, 2) has 1 (1) possible DDs
- (3, 16, 2) has 5 (5) possible DDs
- (4, 16, 2) has 9 (9) possible DDs
- (5, 16, 2) has 16 (18) possible DDs
- (6, 16, 2) has 29 (33) possible DDs
- (7, 16, 2) has 40 (50) possible DDs
- (8, 16, 2) has 59 (77) possible DDs
- (9, 16, 2) has 77 (110) possible DDs
- (10, 16, 2) has 101 (140) possible DDs
- (11, 16, 2) has 128 (194) possible DDs
- (12, 16, 2) has 156 (256) possible DDs
- (13, 16, 2) has 87 (308) possible DDs
- (14, 16, 2) has 40 (406) possible DDs
- (15, 16, 2) has 22 (505) possible DDs
16.32.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 32, 3) has 1 (1) possible DDs
- (4, 32, 3) has 5 (5) possible DDs
- (5, 32, 3) has 9 (9) possible DDs
- (6, 32, 3) has 15 (18) possible DDs
- (7, 32, 3) has 10 (27) possible DDs
- (8, 32, 3) has 18 (47) possible DDs
- (9, 32, 3) has 18 (70) possible DDs
- (10, 32, 3) has 27 (104) possible DDs
- (11, 32, 3) has 17 (141) possible DDs
- (12, 32, 3) has 34 (190) possible DDs
- (13, 32, 3) has 24 (256) possible DDs
- (14, 32, 3) has 16 (338) possible DDs
- (15, 32, 3) has 11 (435) possible DDs
- (16, 32, 3) has 10 (588) possible DDs
Row 9.128.5
6.16.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 16, 2) has 1 (1) possible DDs
- (3, 16, 2) has 5 (5) possible DDs
- (4, 16, 2) has 9 (9) possible DDs
- (5, 16, 2) has 16 (18) possible DDs
- (6, 16, 2) has 29 (33) possible DDs
7.32.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 32, 3) has 1 (1) possible DDs
- (4, 32, 3) has 5 (5) possible DDs
- (5, 32, 3) has 9 (9) possible DDs
- (6, 32, 3) has 15 (18) possible DDs
- (7, 32, 3) has 10 (27) possible DDs
8.64.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 64, 4) has 1 (1) possible DDs
- (5, 64, 4) has 5 (5) possible DDs
- (6, 64, 4) has 9 (9) possible DDs
- (7, 64, 4) has 14 (14) possible DDs
- (8, 64, 4) has 3 (18) possible DDs
9.128.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 128, 5) has 1 (1) possible DDs
- (6, 128, 5) has 5 (5) possible DDs
- (7, 128, 5) has 9 (9) possible DDs
- (8, 128, 5) has 14 (14) possible DDs
- (9, 128, 5) has 2 (16) possible DDs
Row 13.4096.10
5.16.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 16, 2) has 1 (1) possible DDs
- (3, 16, 2) has 5 (5) possible DDs
- (4, 16, 2) has 9 (9) possible DDs
- (5, 16, 2) has 16 (18) possible DDs
6.32.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 32, 3) has 1 (1) possible DDs
- (4, 32, 3) has 5 (5) possible DDs
- (5, 32, 3) has 9 (9) possible DDs
- (6, 32, 3) has 15 (18) possible DDs
7.64.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 64, 4) has 1 (1) possible DDs
- (5, 64, 4) has 5 (5) possible DDs
- (6, 64, 4) has 9 (9) possible DDs
- (7, 64, 4) has 14 (14) possible DDs
8.128.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 128, 5) has 1 (1) possible DDs
- (6, 128, 5) has 5 (5) possible DDs
- (7, 128, 5) has 9 (9) possible DDs
- (8, 128, 5) has 14 (14) possible DDs
9.256.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 256, 6) has 1 (1) possible DDs
- (7, 256, 6) has 5 (5) possible DDs
- (8, 256, 6) has 9 (9) possible DDs
- (9, 256, 6) has 14 (14) possible DDs
10.512.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 512, 7) has 1 (1) possible DDs
- (8, 512, 7) has 5 (5) possible DDs
- (9, 512, 7) has 9 (9) possible DDs
- (10, 512, 7) has 14 (14) possible DDs
11.1024.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 1024, 8) has 1 (1) possible DDs
- (9, 1024, 8) has 5 (5) possible DDs
- (10, 1024, 8) has 9 (9) possible DDs
- (11, 1024, 8) has 14 (14) possible DDs
12.2048.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 2048, 9) has 1 (1) possible DDs
- (10, 2048, 9) has 5 (5) possible DDs
- (11, 2048, 9) has 9 (9) possible DDs
- (12, 2048, 9) has 14 (14) possible DDs
13.4096.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 4096, 10) has 1 (1) possible DDs
- (11, 4096, 10) has 5 (5) possible DDs
- (12, 4096, 10) has 9 (9) possible DDs
- (13, 4096, 10) has 14 (14) possible DDs
Row 20.40.3
19.20.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 20, 2) has 1 (1) possible DDs
- (3, 20, 2) has 6 (6) possible DDs
- (4, 20, 2) has 12 (13) possible DDs
- (5, 20, 2) has 24 (28) possible DDs
- (6, 20, 2) has 50 (60) possible DDs
- (7, 20, 2) has 98 (108) possible DDs
- (8, 20, 2) has 153 (167) possible DDs
- (9, 20, 2) has 230 (269) possible DDs
- (10, 20, 2) has 318 (403) possible DDs
- (11, 20, 2) has 466 (546) possible DDs
- (12, 20, 2) has 563 (752) possible DDs
- (13, 20, 2) has 758 (1036) possible DDs
- (14, 20, 2) has 962 (1347) possible DDs
- (15, 20, 2) has 1264 (1734) possible DDs
- (16, 20, 2) has 1546 (2284) possible DDs
- (17, 20, 2) has 772 (2862) possible DDs
- (18, 20, 2) has 213 (3547) possible DDs
- (19, 20, 2) has 52 (4490) possible DDs
20.40.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 40, 3) has 1 (1) possible DDs
- (4, 40, 3) has 6 (6) possible DDs
- (5, 40, 3) has 10 (12) possible DDs
- (6, 40, 3) has 14 (28) possible DDs
- (7, 40, 3) has 24 (54) possible DDs
- (8, 40, 3) has 34 (106) possible DDs
- (9, 40, 3) has 23 (177) possible DDs
- (10, 40, 3) has 50 (286) possible DDs
- (11, 40, 3) has 37 (415) possible DDs
- (12, 40, 3) has 79 (644) possible DDs
- (13, 40, 3) has 55 (895) possible DDs
- (14, 40, 3) has 91 (1276) possible DDs
- (15, 40, 3) has 80 (1722) possible DDs
- (16, 40, 3) has 137 (2417) possible DDs
- (17, 40, 3) has 102 (3236) possible DDs
- (18, 40, 3) has 58 (4313) possible DDs
- (19, 40, 3) has 29 (5607) possible DDs
- (20, 40, 3) has 15 (7563) possible DDs
Row 24.48.3
TO BE COMPUTED
Row 12.192.5
9.24.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 24, 2) has 1 (1) possible DDs
- (3, 24, 2) has 7 (7) possible DDs
- (4, 24, 2) has 18 (18) possible DDs
- (5, 24, 2) has 45 (49) possible DDs
- (6, 24, 2) has 99 (103) possible DDs
- (7, 24, 2) has 194 (204) possible DDs
- (8, 24, 2) has 342 (358) possible DDs
- (9, 24, 2) has 560 (590) possible DDs
10.48.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 48, 3) has 1 (1) possible DDs
- (4, 48, 3) has 7 (7) possible DDs
- (5, 48, 3) has 17 (17) possible DDs
- (6, 48, 3) has 34 (44) possible DDs
- (7, 48, 3) has 68 (94) possible DDs
- (8, 48, 3) has 147 (206) possible DDs
- (9, 48, 3) has 203 (376) possible DDs
- (10, 48, 3) has 374 (699) possible DDs
11.96.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 96, 4) has 1 (1) possible DDs
- (5, 96, 4) has 7 (7) possible DDs
- (6, 96, 4) has 16 (16) possible DDs
- (7, 96, 4) has 16 (32) possible DDs
- (8, 96, 4) has 20 (75) possible DDs
- (9, 96, 4) has 0 (134) possible DDs
- (10, 96, 4) has 0 (240) possible DDs
- (11, 96, 4) has 0 (406) possible DDs
12.192.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 192, 5) has 1 (1) possible DDs
- (6, 192, 5) has 7 (7) possible DDs
- (7, 192, 5) has 16 (16) possible DDs
- (8, 192, 5) has 12 (33) possible DDs
- (9, 192, 5) has 8 (67) possible DDs
- (10, 192, 5) has 0 (120) possible DDs
- (11, 192, 5) has 0 (216) possible DDs
- (12, 192, 5) has 0 (377) possible DDs
Row 14.6144.10
6.24.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 24, 2) has 1 (1) possible DDs
- (3, 24, 2) has 7 (7) possible DDs
- (4, 24, 2) has 18 (18) possible DDs
- (5, 24, 2) has 45 (49) possible DDs
- (6, 24, 2) has 99 (103) possible DDs
7.48.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 48, 3) has 1 (1) possible DDs
- (4, 48, 3) has 7 (7) possible DDs
- (5, 48, 3) has 17 (17) possible DDs
- (6, 48, 3) has 34 (44) possible DDs
- (7, 48, 3) has 68 (94) possible DDs
8.96.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 96, 4) has 1 (1) possible DDs
- (5, 96, 4) has 7 (7) possible DDs
- (6, 96, 4) has 16 (16) possible DDs
- (7, 96, 4) has 16 (32) possible DDs
- (8, 96, 4) has 20 (75) possible DDs
9.192.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 192, 5) has 1 (1) possible DDs
- (6, 192, 5) has 7 (7) possible DDs
- (7, 192, 5) has 16 (16) possible DDs
- (8, 192, 5) has 12 (33) possible DDs
- (9, 192, 5) has 8 (67) possible DDs
10.384.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 384, 6) has 1 (1) possible DDs
- (7, 384, 6) has 7 (7) possible DDs
- (8, 384, 6) has 16 (16) possible DDs
- (9, 384, 6) has 5 (28) possible DDs
- (10, 384, 6) has 4 (53) possible DDs
11.768.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 768, 7) has 1 (1) possible DDs
- (8, 768, 7) has 7 (7) possible DDs
- (9, 768, 7) has 16 (16) possible DDs
- (10, 768, 7) has 3 (28) possible DDs
- (11, 768, 7) has 2 (51) possible DDs
12.1536.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 1536, 8) has 1 (1) possible DDs
- (9, 1536, 8) has 7 (7) possible DDs
- (10, 1536, 8) has 16 (16) possible DDs
- (11, 1536, 8) has 0 (24) possible DDs
- (12, 1536, 8) has 0 (52) possible DDs
13.3072.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 3072, 9) has 1 (1) possible DDs
- (10, 3072, 9) has 7 (7) possible DDs
- (11, 3072, 9) has 16 (16) possible DDs
- (12, 3072, 9) has 0 (25) possible DDs
- (13, 3072, 9) has 0 (48) possible DDs
14.6144.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 6144, 10) has 1 (1) possible DDs
- (11, 6144, 10) has 7 (7) possible DDs
- (12, 6144, 10) has 16 (16) possible DDs
- (13, 6144, 10) has 0 (20) possible DDs
- (14, 6144, 10) has 0 (42) possible DDs
Row 28.56.3
TO BE COMPUTED
Row 13.224.5
10.28.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 28, 2) has 1 (1) possible DDs
- (3, 28, 2) has 8 (8) possible DDs
- (4, 28, 2) has 21 (22) possible DDs
- (5, 28, 2) has 65 (69) possible DDs
- (6, 28, 2) has 158 (166) possible DDs
- (7, 28, 2) has 332 (350) possible DDs
- (8, 28, 2) has 646 (677) possible DDs
- (9, 28, 2) has 1120 (1211) possible DDs
- (10, 28, 2) has 1833 (1990) possible DDs
11.56.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 56, 3) has 1 (1) possible DDs
- (4, 56, 3) has 8 (8) possible DDs
- (5, 56, 3) has 19 (21) possible DDs
- (6, 56, 3) has 54 (64) possible DDs
- (7, 56, 3) has 112 (154) possible DDs
- (8, 56, 3) has 264 (380) possible DDs
- (9, 56, 3) has 506 (762) possible DDs
- (10, 56, 3) has 883 (1517) possible DDs
- (11, 56, 3) has 1459 (2607) possible DDs
12.112.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 112, 4) has 1 (1) possible DDs
- (5, 112, 4) has 8 (8) possible DDs
- (6, 112, 4) has 16 (20) possible DDs
- (7, 112, 4) has 18 (48) possible DDs
- (8, 112, 4) has 34 (117) possible DDs
- (9, 112, 4) has 33 (230) possible DDs
- (10, 112, 4) has 0 (461) possible DDs
- (11, 112, 4) has 0 (846) possible DDs
- (12, 112, 4) has 0 (1492) possible DDs
13.224.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 224, 5) has 1 (1) possible DDs
- (6, 224, 5) has 8 (8) possible DDs
- (7, 224, 5) has 13 (19) possible DDs
- (8, 224, 5) has 6 (48) possible DDs
- (9, 224, 5) has 9 (110) possible DDs
- (10, 224, 5) has 6 (215) possible DDs
- (11, 224, 5) has 0 (445) possible DDs
- (12, 224, 5) has 0 (815) possible DDs
- (13, 224, 5) has 0 (1506) possible DDs
Row 14.7168.10
6.28.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 28, 2) has 1 (1) possible DDs
- (3, 28, 2) has 8 (8) possible DDs
- (4, 28, 2) has 21 (22) possible DDs
- (5, 28, 2) has 65 (69) possible DDs
- (6, 28, 2) has 158 (166) possible DDs
7.56.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 56, 3) has 1 (1) possible DDs
- (4, 56, 3) has 8 (8) possible DDs
- (5, 56, 3) has 19 (21) possible DDs
- (6, 56, 3) has 54 (64) possible DDs
- (7, 56, 3) has 112 (154) possible DDs
8.112.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 112, 4) has 1 (1) possible DDs
- (5, 112, 4) has 8 (8) possible DDs
- (6, 112, 4) has 16 (20) possible DDs
- (7, 112, 4) has 18 (48) possible DDs
- (8, 112, 4) has 34 (117) possible DDs
9.224.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 224, 5) has 1 (1) possible DDs
- (6, 224, 5) has 8 (8) possible DDs
- (7, 224, 5) has 13 (19) possible DDs
- (8, 224, 5) has 6 (48) possible DDs
- (9, 224, 5) has 9 (110) possible DDs
10.448.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 448, 6) has 1 (1) possible DDs
- (7, 448, 6) has 8 (8) possible DDs
- (8, 448, 6) has 9 (18) possible DDs
- (9, 448, 6) has 0 (41) possible DDs
- (10, 448, 6) has 0 (90) possible DDs
11.896.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 896, 7) has 1 (1) possible DDs
- (8, 896, 7) has 8 (8) possible DDs
- (9, 896, 7) has 5 (17) possible DDs
- (10, 896, 7) has 0 (43) possible DDs
- (11, 896, 7) has 0 (91) possible DDs
12.1792.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 1792, 8) has 1 (1) possible DDs
- (9, 1792, 8) has 8 (8) possible DDs
- (10, 1792, 8) has 0 (16) possible DDs
- (11, 1792, 8) has 0 (40) possible DDs
- (12, 1792, 8) has 0 (82) possible DDs
13.3584.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 3584, 9) has 1 (1) possible DDs
- (10, 3584, 9) has 8 (8) possible DDs
- (11, 3584, 9) has 0 (16) possible DDs
- (12, 3584, 9) has 0 (42) possible DDs
- (13, 3584, 9) has 0 (85) possible DDs
14.7168.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 7168, 10) has 1 (1) possible DDs
- (11, 7168, 10) has 8 (8) possible DDs
- (12, 7168, 10) has 0 (16) possible DDs
- (13, 7168, 10) has 0 (38) possible DDs
- (14, 7168, 10) has 0 (85) possible DDs
Row 32.64.3
TO BE COMPUTED
Row 16.256.5
TO BE CONTINUED..
13.32.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 32, 2) has 1 (1) possible DDs
- (3, 32, 2) has 9 (9) possible DDs
- (4, 32, 2) has 29 (29) possible DDs
- (5, 32, 2) has 89 (93) possible DDs
- (6, 32, 2) has 240 (250) possible DDs
- (7, 32, 2) has 571 (593) possible DDs
- (8, 32, 2) has 1157 (1187) possible DDs
- (9, 32, 2) has 2197 (2282) possible DDs
- (10, 32, 2) has 3947 (4054) possible DDs
- (11, 32, 2) has 6559 (6721) possible DDs
- (12, 32, 2) has 10516 (10738) possible DDs
- (13, 32, 2) has 16307 (16702) possible DDs
14.64.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 64, 3) has 1 (1) possible DDs
- (4, 64, 3) has 9 (9) possible DDs
- (5, 64, 3) has 28 (28) possible DDs
- (6, 64, 3) has 78 (93) possible DDs
- (7, 64, 3) has 205 (249) possible DDs
- (8, 64, 3) has 528 (652) possible DDs
- (9, 64, 3) has 1082 (1426) possible DDs
- (10, 64, 3) has 2289 (3080) possible DDs
- (11, 64, 3) has 4373 (5823) possible DDs
- (12, 64, 3) has ? (10887) possible DDs
- (13, 64, 3) has ? (18609) possible DDs
- (14, 64, 3) has ? (31572) possible DDs
Row 12.1024.7
7.32.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 32, 2) has 1 (1) possible DDs
- (3, 32, 2) has 9 (9) possible DDs
- (4, 32, 2) has 29 (29) possible DDs
- (5, 32, 2) has 89 (93) possible DDs
- (6, 32, 2) has 240 (250) possible DDs
- (7, 32, 2) has 571 (593) possible DDs
8.64.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 64, 3) has 1 (1) possible DDs
- (4, 64, 3) has 9 (9) possible DDs
- (5, 64, 3) has 28 (28) possible DDs
- (6, 64, 3) has 78 (93) possible DDs
- (7, 64, 3) has 205 (249) possible DDs
- (8, 64, 3) has 528 (652) possible DDs
9.128.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 128, 4) has 1 (1) possible DDs
- (5, 128, 4) has 9 (9) possible DDs
- (6, 128, 4) has 25 (25) possible DDs
- (7, 128, 4) has 61 (71) possible DDs
- (8, 128, 4) has 128 (188) possible DDs
- (9, 128, 4) has 205 (378) possible DDs
10.256.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 256, 5) has 1 (1) possible DDs
- (6, 256, 5) has 9 (9) possible DDs
- (7, 256, 5) has 25 (25) possible DDs
- (8, 256, 5) has 59 (72) possible DDs
- (9, 256, 5) has 114 (182) possible DDs
- (10, 256, 5) has 68 (372) possible DDs
11.512.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 512, 6) has 1 (1) possible DDs
- (7, 512, 6) has 9 (9) possible DDs
- (8, 512, 6) has 25 (25) possible DDs
- (9, 512, 6) has 55 (65) possible DDs
- (10, 512, 6) has 106 (148) possible DDs
- (11, 512, 6) has 3 (318) possible DDs
12.1024.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1024, 7) has 1 (1) possible DDs
- (8, 1024, 7) has 9 (9) possible DDs
- (9, 1024, 7) has 25 (25) possible DDs
- (10, 1024, 7) has 55 (65) possible DDs
- (11, 1024, 7) has 106 (145) possible DDs
- (12, 1024, 7) has 2 (300) possible DDs
Row 14.8192.10
6.32.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 32, 2) has 1 (1) possible DDs
- (3, 32, 2) has 9 (9) possible DDs
- (4, 32, 2) has 29 (29) possible DDs
- (5, 32, 2) has 89 (93) possible DDs
- (6, 32, 2) has 240 (250) possible DDs
7.64.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 64, 3) has 1 (1) possible DDs
- (4, 64, 3) has 9 (9) possible DDs
- (5, 64, 3) has 28 (28) possible DDs
- (6, 64, 3) has 78 (93) possible DDs
- (7, 64, 3) has 205 (249) possible DDs
8.128.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 128, 4) has 1 (1) possible DDs
- (5, 128, 4) has 9 (9) possible DDs
- (6, 128, 4) has 25 (25) possible DDs
- (7, 128, 4) has 61 (71) possible DDs
- (8, 128, 4) has 128 (188) possible DDs
9.256.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 256, 5) has 1 (1) possible DDs
- (6, 256, 5) has 9 (9) possible DDs
- (7, 256, 5) has 25 (25) possible DDs
- (8, 256, 5) has 59 (72) possible DDs
- (9, 256, 5) has 114 (182) possible DDs
10.512.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 512, 6) has 1 (1) possible DDs
- (7, 512, 6) has 9 (9) possible DDs
- (8, 512, 6) has 25 (25) possible DDs
- (9, 512, 6) has 55 (65) possible DDs
- (10, 512, 6) has 106 (148) possible DDs
11.1024.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1024, 7) has 1 (1) possible DDs
- (8, 1024, 7) has 9 (9) possible DDs
- (9, 1024, 7) has 25 (25) possible DDs
- (10, 1024, 7) has 55 (65) possible DDs
- (11, 1024, 7) has 106 (145) possible DDs
12.2048.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 2048, 8) has 1 (1) possible DDs
- (9, 2048, 8) has 9 (9) possible DDs
- (10, 2048, 8) has 25 (25) possible DDs
- (11, 2048, 8) has 55 (61) possible DDs
- (12, 2048, 8) has 106 (138) possible DDs
13.4096.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 4096, 9) has 1 (1) possible DDs
- (10, 4096, 9) has 9 (9) possible DDs
- (11, 4096, 9) has 25 (25) possible DDs
- (12, 4096, 9) has 55 (61) possible DDs
- (13, 4096, 9) has 106 (137) possible DDs
14.8192.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 8192, 10) has 1 (1) possible DDs
- (11, 8192, 10) has 9 (9) possible DDs
- (12, 8192, 10) has 25 (25) possible DDs
- (13, 8192, 10) has 55 (61) possible DDs
- (14, 8192, 10) has 106 (142) possible DDs
Row 17.320.5
TO BE COMPUTED
Row 15.10240.10
7.40.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 40, 2) has 1 (1) possible DDs
- (3, 40, 2) has 11 (11) possible DDs
- (4, 40, 2) has 42 (42) possible DDs
- (5, 40, 2) has 164 (170) possible DDs
- (6, 40, 2) has 508 (518) possible DDs
- (7, 40, 2) has 1364 (1402) possible DDs
8.80.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 80, 3) has 1 (1) possible DDs
- (4, 80, 3) has 11 (11) possible DDs
- (5, 80, 3) has 41 (41) possible DDs
- (6, 80, 3) has 142 (167) possible DDs
- (7, 80, 3) has 472 (534) possible DDs
- (8, 80, 3) has 1401 (1660) possible DDs
9.160.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 160, 4) has 1 (1) possible DDs
- (5, 160, 4) has 11 (11) possible DDs
- (6, 160, 4) has 38 (38) possible DDs
- (7, 160, 4) has 94 (126) possible DDs
- (8, 160, 4) has 221 (389) possible DDs
- (9, 160, 4) has 608 (946) possible DDs
10.320.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 320, 5) has 1 (1) possible DDs
- (6, 320, 5) has 11 (11) possible DDs
- (7, 320, 5) has 37 (37) possible DDs
- (8, 320, 5) has 78 (124) possible DDs
- (9, 320, 5) has 111 (378) possible DDs
- (10, 320, 5) has 348 (974) possible DDs
11.640.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 640, 6) has 1 (1) possible DDs
- (7, 640, 6) has 11 (11) possible DDs
- (8, 640, 6) has 36 (36) possible DDs
- (9, 640, 6) has 61 (111) possible DDs
- (10, 640, 6) has 18 (319) possible DDs
- (11, 640, 6) has 32 (807) possible DDs
12.1280.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1280, 7) has 1 (1) possible DDs
- (8, 1280, 7) has 11 (11) possible DDs
- (9, 1280, 7) has 36 (36) possible DDs
- (10, 1280, 7) has 42 (110) possible DDs
- (11, 1280, 7) has 5 (311) possible DDs
- (12, 1280, 7) has 4 (795) possible DDs
13.2560.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 2560, 8) has 1 (1) possible DDs
- (9, 2560, 8) has 11 (11) possible DDs
- (10, 2560, 8) has 36 (36) possible DDs
- (11, 2560, 8) has 24 (103) possible DDs
- (12, 2560, 8) has 0 (281) possible DDs
- (13, 2560, 8) has 0 (690) possible DDs
14.5120.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 5120, 9) has 1 (1) possible DDs
- (10, 5120, 9) has 11 (11) possible DDs
- (11, 5120, 9) has 36 (36) possible DDs
- (12, 5120, 9) has 17 (102) possible DDs
- (13, 5120, 9) has 0 (269) possible DDs
- (14, 5120, 9) has 0 (678) possible DDs
15.10240.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 10240, 10) has 1 (1) possible DDs
- (11, 10240, 10) has 11 (11) possible DDs
- (12, 10240, 10) has 36 (36) possible DDs
- (13, 10240, 10) has 7 (97) possible DDs
- (14, 10240, 10) has 0 (250) possible DDs
- (15, 10240, 10) has 0 (619) possible DDs
Row 17.352.5
TO BE COMPUTED
Row 15.11264.10
7.44.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 44, 2) has 1 (1) possible DDs
- (3, 44, 2) has 12 (12) possible DDs
- (4, 44, 2) has 49 (50) possible DDs
- (5, 44, 2) has 210 (216) possible DDs
- (6, 44, 2) has 689 (711) possible DDs
- (7, 44, 2) has 2030 (2072) possible DDs
8.88.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 88, 3) has 1 (1) possible DDs
- (4, 88, 3) has 12 (12) possible DDs
- (5, 88, 3) has 46 (48) possible DDs
- (6, 88, 3) has 187 (215) possible DDs
- (7, 88, 3) has 648 (738) possible DDs
- (8, 88, 3) has 2176 (2499) possible DDs
9.176.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 176, 4) has 1 (1) possible DDs
- (5, 176, 4) has 12 (12) possible DDs
- (6, 176, 4) has 40 (44) possible DDs
- (7, 176, 4) has 106 (158) possible DDs
- (8, 176, 4) has 340 (550) possible DDs
- (9, 176, 4) has 1084 (1408) possible DDs
10.352.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 352, 5) has 1 (1) possible DDs
- (6, 352, 5) has 12 (12) possible DDs
- (7, 352, 5) has 37 (43) possible DDs
- (8, 352, 5) has 77 (159) possible DDs
- (9, 352, 5) has 230 (537) possible DDs
- (10, 352, 5) has 771 (1464) possible DDs
11.704.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 704, 6) has 1 (1) possible DDs
- (7, 704, 6) has 12 (12) possible DDs
- (8, 704, 6) has 33 (42) possible DDs
- (9, 704, 6) has 41 (142) possible DDs
- (10, 704, 6) has 90 (432) possible DDs
- (11, 704, 6) has 250 (1251) possible DDs
12.1408.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1408, 7) has 1 (1) possible DDs
- (8, 1408, 7) has 12 (12) possible DDs
- (9, 1408, 7) has 29 (41) possible DDs
- (10, 1408, 7) has 20 (141) possible DDs
- (11, 1408, 7) has 24 (420) possible DDs
- (12, 1408, 7) has 54 (1224) possible DDs
13.2816.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 2816, 8) has 1 (1) possible DDs
- (9, 2816, 8) has 12 (12) possible DDs
- (10, 2816, 8) has 24 (40) possible DDs
- (11, 2816, 8) has 0 (130) possible DDs
- (12, 2816, 8) has 0 (382) possible DDs
- (13, 2816, 8) has 0 (1036) possible DDs
14.5632.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 5632, 9) has 1 (1) possible DDs
- (10, 5632, 9) has 12 (12) possible DDs
- (11, 5632, 9) has 19 (39) possible DDs
- (12, 5632, 9) has 0 (132) possible DDs
- (13, 5632, 9) has 0 (377) possible DDs
- (14, 5632, 9) has 0 (1033) possible DDs
15.11264.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 11264, 10) has 1 (1) possible DDs
- (11, 11264, 10) has 12 (12) possible DDs
- (12, 11264, 10) has 13 (38) possible DDs
- (13, 11264, 10) has 0 (126) possible DDs
- (14, 11264, 10) has 0 (353) possible DDs
- (15, 11264, 10) has 0 (944) possible DDs
Row 18.384.5
TO BE COMPUTED
Row 13.1536.7
8.48.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 48, 2) has 1 (1) possible DDs
- (3, 48, 2) has 13 (13) possible DDs
- (4, 48, 2) has 59 (59) possible DDs
- (5, 48, 2) has 271 (279) possible DDs
- (6, 48, 2) has 942 (954) possible DDs
- (7, 48, 2) has 2898 (2952) possible DDs
- (8, 48, 2) has 7542 (7624) possible DDs
9.96.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 96, 3) has 1 (1) possible DDs
- (4, 96, 3) has 13 (13) possible DDs
- (5, 96, 3) has 57 (57) possible DDs
- (6, 96, 3) has 250 (274) possible DDs
- (7, 96, 3) has 921 (1015) possible DDs
- (8, 96, 3) has 3257 (3651) possible DDs
- (9, 96, 3) has 9565 (10548) possible DDs
10.192.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 192, 4) has 1 (1) possible DDs
- (5, 192, 4) has 13 (13) possible DDs
- (6, 192, 4) has 53 (53) possible DDs
- (7, 192, 4) has 182 (204) possible DDs
- (8, 192, 4) has 526 (731) possible DDs
- (9, 192, 4) has 1656 (2033) possible DDs
- (10, 192, 4) has 4543 (5560) possible DDs
11.384.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 384, 5) has 1 (1) possible DDs
- (6, 384, 5) has 13 (13) possible DDs
- (7, 384, 5) has 52 (52) possible DDs
- (8, 384, 5) has 175 (204) possible DDs
- (9, 384, 5) has 399 (722) possible DDs
- (10, 384, 5) has 1364 (2106) possible DDs
- (11, 384, 5) has 3920 (6213) possible DDs
12.768.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 768, 6) has 1 (1) possible DDs
- (7, 768, 6) has 13 (13) possible DDs
- (8, 768, 6) has 49 (49) possible DDs
- (9, 768, 6) has 158 (182) possible DDs
- (10, 768, 6) has 228 (582) possible DDs
- (11, 768, 6) has 704 (1755) possible DDs
- (12, 768, 6) has 1958 (4499) possible DDs
13.1536.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1536, 7) has 1 (1) possible DDs
- (8, 1536, 7) has 13 (13) possible DDs
- (9, 1536, 7) has 49 (49) possible DDs
- (10, 1536, 7) has 155 (185) possible DDs
- (11, 1536, 7) has 141 (576) possible DDs
- (12, 1536, 7) has 395 (1775) possible DDs
- (13, 1536, 7) has 697 (4626) possible DDs
Row 15.12288.10
7.48.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 48, 2) has 1 (1) possible DDs
- (3, 48, 2) has 13 (13) possible DDs
- (4, 48, 2) has 59 (59) possible DDs
- (5, 48, 2) has 271 (279) possible DDs
- (6, 48, 2) has 942 (954) possible DDs
- (7, 48, 2) has 2898 (2952) possible DDs
8.96.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 96, 3) has 1 (1) possible DDs
- (4, 96, 3) has 13 (13) possible DDs
- (5, 96, 3) has 57 (57) possible DDs
- (6, 96, 3) has 250 (274) possible DDs
- (7, 96, 3) has 921 (1015) possible DDs
- (8, 96, 3) has 3257 (3651) possible DDs
9.192.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 192, 4) has 1 (1) possible DDs
- (5, 192, 4) has 13 (13) possible DDs
- (6, 192, 4) has 53 (53) possible DDs
- (7, 192, 4) has 182 (204) possible DDs
- (8, 192, 4) has 526 (731) possible DDs
- (9, 192, 4) has 1656 (2033) possible DDs
10.384.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 384, 5) has 1 (1) possible DDs
- (6, 384, 5) has 13 (13) possible DDs
- (7, 384, 5) has 52 (52) possible DDs
- (8, 384, 5) has 175 (204) possible DDs
- (9, 384, 5) has 399 (722) possible DDs
- (10, 384, 5) has 1364 (2106) possible DDs
11.768.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 768, 6) has 1 (1) possible DDs
- (7, 768, 6) has 13 (13) possible DDs
- (8, 768, 6) has 49 (49) possible DDs
- (9, 768, 6) has 158 (182) possible DDs
- (10, 768, 6) has 228 (582) possible DDs
- (11, 768, 6) has 704 (1755) possible DDs
12.1536.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1536, 7) has 1 (1) possible DDs
- (8, 1536, 7) has 13 (13) possible DDs
- (9, 1536, 7) has 49 (49) possible DDs
- (10, 1536, 7) has 155 (185) possible DDs
- (11, 1536, 7) has 141 (576) possible DDs
- (12, 1536, 7) has 395 (1775) possible DDs
13.3072.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 3072, 8) has 1 (1) possible DDs
- (9, 3072, 8) has 13 (13) possible DDs
- (10, 3072, 8) has 49 (49) possible DDs
- (11, 3072, 8) has 148 (176) possible DDs
- (12, 3072, 8) has 73 (517) possible DDs
- (13, 3072, 8) has 84 (1530) possible DDs
14.6144.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 6144, 9) has 1 (1) possible DDs
- (10, 6144, 9) has 13 (13) possible DDs
- (11, 6144, 9) has 49 (49) possible DDs
- (12, 6144, 9) has 147 (173) possible DDs
- (13, 6144, 9) has 17 (511) possible DDs
- (14, 6144, 9) has 20 (1522) possible DDs
15.12288.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 12288, 10) has 1 (1) possible DDs
- (11, 12288, 10) has 13 (13) possible DDs
- (12, 12288, 10) has 49 (49) possible DDs
- (13, 12288, 10) has 146 (168) possible DDs
- (14, 12288, 10) has 5 (494) possible DDs
- (15, 12288, 10) has 4 (1376) possible DDs
Row 19.416.5
TO BE COMPUTED
Row 13.1664.7
TO BE CONTINUED
8.52.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 52, 2) has 1 (1) possible DDs
- (3, 52, 2) has 14 (14) possible DDs
- (4, 52, 2) has 66 (67) possible DDs
- (5, 52, 2) has 331 (341) possible DDs
- (6, 52, 2) has 1234 (1256) possible DDs
- (7, 52, 2) has 4046 (4100) possible DDs
- (8, 52, 2) has ? (11199) possible DDs
9.104.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 104, 3) has 1 (1) possible DDs
- (4, 104, 3) has 14 (14) possible DDs
- (5, 104, 3) has 63 (65) possible DDs
- (6, 104, 3) has 298 (342) possible DDs
- (7, 104, 3) has 1232 (1348) possible DDs
- (8, 104, 3) has 4630 (5184) possible DDs
- (9, 104, 3) has ? (15902) possible DDs
10.208.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 208, 4) has 1 (1) possible DDs
- (5, 208, 4) has 14 (14) possible DDs
- (6, 208, 4) has 55 (59) possible DDs
- (7, 208, 4) has 196 (252) possible DDs
- (8, 208, 4) has 718 (974) possible DDs
- (9, 208, 4) has 2331 (2823) possible DDs
- (10, 208, 4) has ? (8134) possible DDs
11.416.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 416, 5) has 1 (1) possible DDs
- (6, 416, 5) has 14 (14) possible DDs
- (7, 416, 5) has 52 (58) possible DDs
- (8, 416, 5) has 167 (253) possible DDs
- (9, 416, 5) has 576 (978) possible DDs
- (10, 416, 5) has 1965 (3006) possible DDs
- (11, 416, 5) has ? (9342) possible DDs
12.832.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 832, 6) has 1 (1) possible DDs
- (7, 832, 6) has 14 (14) possible DDs
- (8, 832, 6) has 48 (57) possible DDs
- (9, 832, 6) has 106 (228) possible DDs
- (10, 832, 6) has 317 (769) possible DDs
- (11, 832, 6) has 1100 (2511) possible DDs
- (12, 832, 6) has ? (6481) possible DDs
13.1664.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1664, 7) has 1 (1) possible DDs
- (8, 1664, 7) has 14 (14) possible DDs
- (9, 1664, 7) has 44 (56) possible DDs
- (10, 1664, 7) has 73 (223) possible DDs
- (11, 1664, 7) has 193 (761) possible DDs
- (12, 1664, 7) has 698 (2528) possible DDs
- (13, 1664, 7) has ? (6806) possible DDs
Row 15.13312.10
7.52.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 52, 2) has 1 (1) possible DDs
- (3, 52, 2) has 14 (14) possible DDs
- (4, 52, 2) has 66 (67) possible DDs
- (5, 52, 2) has 331 (341) possible DDs
- (6, 52, 2) has 1234 (1256) possible DDs
- (7, 52, 2) has 4046 (4100) possible DDs
8.104.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 104, 3) has 1 (1) possible DDs
- (4, 104, 3) has 14 (14) possible DDs
- (5, 104, 3) has 63 (65) possible DDs
- (6, 104, 3) has 298 (342) possible DDs
- (7, 104, 3) has 1232 (1348) possible DDs
- (8, 104, 3) has 4630 (5184) possible DDs
9.208.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 208, 4) has 1 (1) possible DDs
- (5, 208, 4) has 14 (14) possible DDs
- (6, 208, 4) has 55 (59) possible DDs
- (7, 208, 4) has 196 (252) possible DDs
- (8, 208, 4) has 718 (974) possible DDs
- (9, 208, 4) has 2331 (2823) possible DDs
10.416.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 416, 5) has 1 (1) possible DDs
- (6, 416, 5) has 14 (14) possible DDs
- (7, 416, 5) has 52 (58) possible DDs
- (8, 416, 5) has 167 (253) possible DDs
- (9, 416, 5) has 576 (978) possible DDs
- (10, 416, 5) has 1965 (3006) possible DDs
11.832.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 832, 6) has 1 (1) possible DDs
- (7, 832, 6) has 14 (14) possible DDs
- (8, 832, 6) has 48 (57) possible DDs
- (9, 832, 6) has 106 (228) possible DDs
- (10, 832, 6) has 317 (769) possible DDs
- (11, 832, 6) has 1100 (2511) possible DDs
12.1664.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1664, 7) has 1 (1) possible DDs
- (8, 1664, 7) has 14 (14) possible DDs
- (9, 1664, 7) has 44 (56) possible DDs
- (10, 1664, 7) has 73 (223) possible DDs
- (11, 1664, 7) has 193 (761) possible DDs
- (12, 1664, 7) has 698 (2528) possible DDs
13.3328.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 3328, 8) has 1 (1) possible DDs
- (9, 3328, 8) has 14 (14) possible DDs
- (10, 3328, 8) has 39 (55) possible DDs
- (11, 3328, 8) has 36 (212) possible DDs
- (12, 3328, 8) has 91 (683) possible DDs
- (13, 3328, 8) has 174 (2134) possible DDs
14.6656.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 6656, 9) has 1 (1) possible DDs
- (10, 6656, 9) has 14 (14) possible DDs
- (11, 6656, 9) has 34 (54) possible DDs
- (12, 6656, 9) has 10 (209) possible DDs
- (13, 6656, 9) has 19 (681) possible DDs
- (14, 6656, 9) has 23 (2180) possible DDs
15.13312.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 13312, 10) has 1 (1) possible DDs
- (11, 13312, 10) has 14 (14) possible DDs
- (12, 13312, 10) has 28 (53) possible DDs
- (13, 13312, 10) has 0 (200) possible DDs
- (14, 13312, 10) has 0 (651) possible DDs
- (15, 13312, 10) has 0 (1970) possible DDs
Row 20.448.5
TO BE COMPUTED
Row 13.1792.7
TO BE CONTINUED
8.56.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 56, 2) has 1 (1) possible DDs
- (3, 56, 2) has 15 (15) possible DDs
- (4, 56, 2) has 78 (78) possible DDs
- (5, 56, 2) has 405 (413) possible DDs
- (6, 56, 2) has 1596 (1620) possible DDs
- (7, 56, 2) has 5554 (5622) possible DDs
- (8, 56, 2) has ? (15984) possible DDs
9.112.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 112, 3) has 1 (1) possible DDs
- (4, 112, 3) has 15 (15) possible DDs
- (5, 112, 3) has 76 (76) possible DDs
- (6, 112, 3) has 375 (420) possible DDs
- (7, 112, 3) has 1648 (1766) possible DDs
- (8, 112, 3) has 6626 (7206) possible DDs
- (9, 112, 3) has ? (23350) possible DDs
10.224.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 224, 4) has 1 (1) possible DDs
- (5, 224, 4) has 15 (15) possible DDs
- (6, 224, 4) has 70 (70) possible DDs
- (7, 224, 4) has 259 (311) possible DDs
- (8, 224, 4) has 996 (1258) possible DDs
- (9, 224, 4) has 3268 (3806) possible DDs
- (10, 224, 4) has ? (11589) possible DDs
11.448.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 448, 5) has 1 (1) possible DDs
- (6, 448, 5) has 15 (15) possible DDs
- (7, 448, 5) has 69 (69) possible DDs
- (8, 448, 5) has 238 (309) possible DDs
- (9, 448, 5) has 817 (1291) possible DDs
- (10, 448, 5) has 2847 (4197) possible DDs
- (11, 448, 5) has ? (13736) possible DDs
12.896.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 896, 6) has 1 (1) possible DDs
- (7, 896, 6) has 15 (15) possible DDs
- (8, 896, 6) has 66 (66) possible DDs
- (9, 896, 6) has 193 (275) possible DDs
- (10, 896, 6) has 539 (1009) possible DDs
- (11, 896, 6) has 1670 (3433) possible DDs
- (12, 896, 6) has ? (9473) possible DDs
13.1792.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1792, 7) has 1 (1) possible DDs
- (8, 1792, 7) has 15 (15) possible DDs
- (9, 1792, 7) has 65 (65) possible DDs
- (10, 1792, 7) has 165 (277) possible DDs
- (11, 1792, 7) has 419 (1018) possible DDs
- (12, 1792, 7) has 1153 (3513) possible DDs
- (13, 1792, 7) has ? (9906) possible DDs
Row 15.14336.10
7.56.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 56, 2) has 1 (1) possible DDs
- (3, 56, 2) has 15 (15) possible DDs
- (4, 56, 2) has 78 (78) possible DDs
- (5, 56, 2) has 405 (413) possible DDs
- (6, 56, 2) has 1596 (1620) possible DDs
- (7, 56, 2) has 5554 (5622) possible DDs
8.112.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 112, 3) has 1 (1) possible DDs
- (4, 112, 3) has 15 (15) possible DDs
- (5, 112, 3) has 76 (76) possible DDs
- (6, 112, 3) has 375 (420) possible DDs
- (7, 112, 3) has 1648 (1766) possible DDs
- (8, 112, 3) has 6626 (7206) possible DDs
9.224.4, W = P ∪ Q , (all =
internal∪ external)
- (4, 224, 4) has 1 (1) possible DDs
- (5, 224, 4) has 15 (15) possible DDs
- (6, 224, 4) has 70 (70) possible DDs
- (7, 224, 4) has 259 (311) possible DDs
- (8, 224, 4) has 996 (1258) possible DDs
- (9, 224, 4) has 3268 (3806) possible DDs
10.448.5, W = P ∪ Q , (all =
internal∪ external)
- (5, 448, 5) has 1 (1) possible DDs
- (6, 448, 5) has 15 (15) possible DDs
- (7, 448, 5) has 69 (69) possible DDs
- (8, 448, 5) has 238 (309) possible DDs
- (9, 448, 5) has 817 (1291) possible DDs
- (10, 448, 5) has 2847 (4197) possible DDs
11.896.6, W = P ∪ Q , (all =
internal∪ external)
- (6, 896, 6) has 1 (1) possible DDs
- (7, 896, 6) has 15 (15) possible DDs
- (8, 896, 6) has 66 (66) possible DDs
- (9, 896, 6) has 193 (275) possible DDs
- (10, 896, 6) has 539 (1009) possible DDs
- (11, 896, 6) has 1670 (3433) possible DDs
12.1792.7, W = P ∪ Q , (all =
internal∪ external)
- (7, 1792, 7) has 1 (1) possible DDs
- (8, 1792, 7) has 15 (15) possible DDs
- (9, 1792, 7) has 65 (65) possible DDs
- (10, 1792, 7) has 165 (277) possible DDs
- (11, 1792, 7) has 419 (1018) possible DDs
- (12, 1792, 7) has 1153 (3513) possible DDs
13.3584.8, W = P ∪ Q , (all =
internal∪ external)
- (8, 3584, 8) has 1 (1) possible DDs
- (9, 3584, 8) has 15 (15) possible DDs
- (10, 3584, 8) has 64 (64) possible DDs
- (11, 3584, 8) has 134 (252) possible DDs
- (12, 3584, 8) has 270 (910) possible DDs
- (13, 3584, 8) has 632 (3021) possible DDs
14.7168.9, W = P ∪ Q , (all =
internal∪ external)
- (9, 7168, 9) has 1 (1) possible DDs
- (10, 7168, 9) has 15 (15) possible DDs
- (11, 7168, 9) has 64 (64) possible DDs
- (12, 7168, 9) has 106 (255) possible DDs
- (13, 7168, 9) has 150 (908) possible DDs
- (14, 7168, 9) has 349 (3045) possible DDs
15.14336.10, W = P ∪ Q , (all =
internal∪ external)
- (10, 14336, 10) has 1 (1) possible DDs
- (11, 14336, 10) has 15 (15) possible DDs
- (12, 14336, 10) has 64 (64) possible DDs
- (13, 14336, 10) has 83 (246) possible DDs
- (14, 14336, 10) has 21 (849) possible DDs
- (15, 14336, 10) has 56 (2739) possible DDs
Row 21.480.5
TO BE COMPUTED
Row 13.1920.7
TO BE COMPUTED
Row 15.15360.10
TO BE CONTINUED
7.60.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 60, 2) has 1 (1) possible DDs
- (3, 60, 2) has 16 (16) possible DDs
- (4, 60, 2) has 87 (88) possible DDs
- (5, 60, 2) has 498 (508) possible DDs
- (6, 60, 2) has 2036 (2066) possible DDs
- (7, 60, 2) has 7452 (7518) possible DDs
8.120.3, W = P ∪ Q , (all =
internal∪ external)
- (3, 120, 3) has 1 (1) possible DDs
- (4, 120, 3) has 16 (16) possible DDs
- (5, 120, 3) has 83 (85) possible DDs
- (6, 120, 3) has 473 (508) possible DDs
- (7, 120, 3) has ? (2270) possible DDs
- (8, 120, 3) has ? (9810) possible DDs
Row 21.512.5
TO BE COMPUTED
Row 16.2048.7
TO BE COMPUTED
Row 15.16384.10
TO BE CONTINUED
7.64.2, W = P ∪ Q , (all =
internal∪ external)
- (2, 64, 2) has 1 (1) possible DDs
- (3, 64, 2) has 17 (17) possible DDs
- (4, 64, 2) has 99 (99) possible DDs
- (5, 64, 2) has 590 (600) possible DDs
- (6, 64, 2) has 2573 (2591) possible DDs
- (7, 64, 2) has ? (9895) possible DDs
Will be available soon.
For all of the arrays listed in Sloane's Library of Orthogonal Arrays
we have computed their distance distributions (acording an internal and an external point) and we have checked that
these distributions are in the remaining sets W = P ∪ Q.
For some of them in W are remained only their distributions. For others in P remain only the distance distributions acording their internal points.
[1] A. Hedayat, N. J. A. Sloane, J. Stufken, Orthogonal Arrays: Theory and Applications, Springer-Verlag, New York, (1999).
[2] P. Boyvalenkov, H. Kulina, Investigation of binary orthogonal arrays via their distance distributions, Problems of Information Transmission, 49(4), 320-330 (2013).
[3] P. Boyvalenkov, H. Kulina, T. Marinova, M. Stoyanova, Nonexistence of binary orthogonal arrays via their distance distributions, Problems of Information Transmission, 51(4), 326-334 (2015).
[4] P. Boyvalenkov, T. Marinova, M. Stoyanova, Nonexistence of (9; 96; 4) and (10; 112; 4) binary orthogonal arrays, Proc. Fifteenth International Workshop on Algebraic and Combinatorial Cotding Theory, Albena, Bulgaria,
June 18-24, (2016)
Authors: T. Marinova, M. Stoynova
Last modified: 28.05.2016