A Library of Distance Distributions of Binary Orthogonal Arrays
This library contains the results from the distance distributions algorithm including part 2, described in [4].
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 , (← W_ndda_1 = P_ndda_1 ∪ Q_ndda_1 ← all = internal ∪ external) where
W = P ∪ Q are the reduced distance distributions using both part 1 and part 2 of the algorithm. Part 2 is described in [4]
W_ndda_1 = P_ndda_1 ∪ Q_ndda_1 are the reduced distance distributions as described in [4] (part 1)
all = internal ∪ external are the all possible DDs which are generated as in [2] and [3]
More reduced distance distributions without using the second part could be found in BOA LIBRARY - NDDA
Contents:
Row 8.16.3
7.8.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 8, 2) has 1 (← 1 ← 1) possible DDs
- (3, 8, 2) has 3 (← 3 ← 3) possible DDs
- (4, 8, 2) has 4 (← 4 ← 4) possible DDs
- (5, 8, 2) has 3 (← 3 ← 3) possible DDs
- (6, 8, 2) has 3 (← 3 ← 5) possible DDs
- (7, 8, 2) has 4 (← 4 ← 8) possible DDs
8.16.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 16, 3) has 1 (← 1 ← 1) possible DDs
- (4, 16, 3) has 3 (← 3 ← 3) possible DDs
- (5, 16, 3) has 4 (← 4 ← 4) possible DDs
- (6, 16, 3) has 2 (← 2 ← 3) possible DDs
- (7, 16, 3) has 2 (← 2 ← 4) possible DDs
- (8, 16, 3) has 3 (← 3 ← 7) possible DDs
Row 12.24.3
11.12.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 12, 2) has 1 (← 1 ← 1) possible DDs
- (3, 12, 2) has 4 (← 4 ← 4) possible DDs
- (4, 12, 2) has 5 (← 5 ← 6) possible DDs
- (5, 12, 2) has 10 (← 10 ← 12) possible DDs
- (6, 12, 2) has 11 (← 11 ← 17) possible DDs
- (7, 12, 2) has 14 (← 14 ← 20) possible DDs
- (8, 12, 2) has 18 (← 18 ← 29) possible DDs
- (9, 12, 2) has 13 (← 13 ← 36) possible DDs
- (10, 12, 2) has 8 (← 8 ← 46) possible DDs
- (11, 12, 2) has 8 (← 8 ← 58) possible DDs
12.24.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 24, 3) has 1 (← 1 ← 1) possible DDs
- (4, 24, 3) has 4 (← 4 ← 4) possible DDs
- (5, 24, 3) has 3 (← 3 ← 5) possible DDs
- (6, 24, 3) has 6 (← 6 ← 9) possible DDs
- (7, 24, 3) has 4 (← 4 ← 12) possible DDs
- (8, 24, 3) has 7 (← 7 ← 18) possible DDs
- (9, 24, 3) has 7 (← 7 ← 22) possible DDs
- (10, 24, 3) has 5 (← 5 ← 35) possible DDs
- (11, 24, 3) has 4 (← 4 ← 35) possible DDs
- (12, 24, 3) has 5 (← 5 ← 50) possible DDs
Row 16.32.3
15.16.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 16, 2) has 1 (← 1 ← 1) possible DDs
- (3, 16, 2) has 5 (← 5 ← 5) possible DDs
- (4, 16, 2) has 9 (← 9 ← 9) possible DDs
- (5, 16, 2) has 16 (← 16 ← 18) possible DDs
- (6, 16, 2) has 29 (← 29 ← 33) possible DDs
- (7, 16, 2) has 40 (← 40 ← 50) possible DDs
- (8, 16, 2) has 59 (← 59 ← 77) possible DDs
- (9, 16, 2) has 77 (← 77 ← 110) possible DDs
- (10, 16, 2) has 101 (← 101 ← 140) possible DDs
- (11, 16, 2) has 128 (← 128 ← 194) possible DDs
- (12, 16, 2) has 156 (← 156 ← 256) possible DDs
- (13, 16, 2) has 87 (← 87 ← 308) possible DDs
- (14, 16, 2) has 40 (← 40 ← 406) possible DDs
- (15, 16, 2) has 22 (← 22 ← 505) possible DDs
16.32.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 32, 3) has 1 (← 1 ← 1) possible DDs
- (4, 32, 3) has 5 (← 5 ← 5) possible DDs
- (5, 32, 3) has 9 (← 9 ← 9) possible DDs
- (6, 32, 3) has 15 (← 15 ← 18) possible DDs
- (7, 32, 3) has 10 (← 10 ← 27) possible DDs
- (8, 32, 3) has 18 (← 18 ← 47) possible DDs
- (9, 32, 3) has 18 (← 18 ← 70) possible DDs
- (10, 32, 3) has 27 (← 27 ← 104) possible DDs
- (11, 32, 3) has 17 (← 17 ← 141) possible DDs
- (12, 32, 3) has 34 (← 34 ← 190) possible DDs
- (13, 32, 3) has 24 (← 24 ← 256) possible DDs
- (14, 32, 3) has 16 (← 16 ← 338) possible DDs
- (15, 32, 3) has 11 (← 11 ← 435) possible DDs
- (16, 32, 3) has 10 (← 10 ← 588) possible DDs
Row 9.128.5
6.16.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 16, 2) has 1 (← 1 ← 1) possible DDs
- (3, 16, 2) has 5 (← 5 ← 5) possible DDs
- (4, 16, 2) has 9 (← 9 ← 9) possible DDs
- (5, 16, 2) has 16 (← 16 ← 18) possible DDs
- (6, 16, 2) has 29 (← 29 ← 33) possible DDs
7.32.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 32, 3) has 1 (← 1 ← 1) possible DDs
- (4, 32, 3) has 5 (← 5 ← 5) possible DDs
- (5, 32, 3) has 9 (← 9 ← 9) possible DDs
- (6, 32, 3) has 15 (← 15 ← 18) possible DDs
- (7, 32, 3) has 10 (← 10 ← 27) possible DDs
8.64.4, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (4, 64, 4) has 1 (← 1 ← 1) possible DDs
- (5, 64, 4) has 5 (← 5 ← 5) possible DDs
- (6, 64, 4) has 9 (← 9 ← 9) possible DDs
- (7, 64, 4) has 14 (← 14 ← 14) possible DDs
- (8, 64, 4) has 3 (← 3 ← 18) possible DDs
9.128.5, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (5, 128, 5) has 1 (← 1 ← 1) possible DDs
- (6, 128, 5) has 5 (← 5 ← 5) possible DDs
- (7, 128, 5) has 9 (← 9 ← 9) possible DDs
- (8, 128, 5) has 14 (← 14 ← 14) possible DDs
- (9, 128, 5) has 2 (← 2 ← 16) possible DDs
Row 13.4096.10
5.16.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 16, 2) has 1 (← 1 ← 1) possible DDs
- (3, 16, 2) has 5 (← 5 ← 5) possible DDs
- (4, 16, 2) has 9 (← 9 ← 9) possible DDs
- (5, 16, 2) has 16 (← 16 ← 18) possible DDs
6.32.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 32, 3) has 1 (← 1 ← 1) possible DDs
- (4, 32, 3) has 5 (← 5 ← 5) possible DDs
- (5, 32, 3) has 9 (← 9 ← 9) possible DDs
- (6, 32, 3) has 15 (← 15 ← 18) possible DDs
7.64.4, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (4, 64, 4) has 1 (← 1 ← 1) possible DDs
- (5, 64, 4) has 5 (← 5 ← 5) possible DDs
- (6, 64, 4) has 9 (← 9 ← 9) possible DDs
- (7, 64, 4) has 14 (← 14 ← 14) possible DDs
8.128.5, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (5, 128, 5) has 1 (← 1 ← 1) possible DDs
- (6, 128, 5) has 5 (← 5 ← 5) possible DDs
- (7, 128, 5) has 9 (← 9 ← 9) possible DDs
- (8, 128, 5) has 14 (← 14 ← 14) possible DDs
9.256.6, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (6, 256, 6) has 1 (← 1 ← 1) possible DDs
- (7, 256, 6) has 5 (← 5 ← 5) possible DDs
- (8, 256, 6) has 9 (← 9 ← 9) possible DDs
- (9, 256, 6) has 14 (← 14 ← 14) possible DDs
10.512.7, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (7, 512, 7) has 1 (← 1 ← 1) possible DDs
- (8, 512, 7) has 5 (← 5 ← 5) possible DDs
- (9, 512, 7) has 9 (← 9 ← 9) possible DDs
- (10, 512, 7) has 14 (← 14 ← 14) possible DDs
11.1024.8, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (8, 1024, 8) has 1 (← 1 ← 1) possible DDs
- (9, 1024, 8) has 5 (← 5 ← 5) possible DDs
- (10, 1024, 8) has 9 (← 9 ← 9) possible DDs
- (11, 1024, 8) has 14 (← 14 ← 14) possible DDs
12.2048.9, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (9, 2048, 9) has 1 (← 1 ← 1) possible DDs
- (10, 2048, 9) has 5 (← 5 ← 5) possible DDs
- (11, 2048, 9) has 9 (← 9 ← 9) possible DDs
- (12, 2048, 9) has 14 (← 14 ← 14) possible DDs
13.4096.10, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (10, 4096, 10) has 1 (← 1 ← 1) possible DDs
- (11, 4096, 10) has 5 (← 5 ← 5) possible DDs
- (12, 4096, 10) has 9 (← 9 ← 9) possible DDs
- (13, 4096, 10) has 14 (← 14 ← 14) possible DDs
Row 20.40.3
19.20.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 20, 2) has 1 (← 1 ← 1) possible DDs
- (3, 20, 2) has 6 (← 6 ← 6) possible DDs
- (4, 20, 2) has 12 (← 12 ← 13) possible DDs
- (5, 20, 2) has 24 (← 24 ← 28) possible DDs
- (6, 20, 2) has 50 (← 50 ← 60) possible DDs
- (7, 20, 2) has 98 (← 98 ← 108) possible DDs
- (8, 20, 2) has 153 (← 153 ← 167) possible DDs
- (9, 20, 2) has 230 (← 230 ← 269) possible DDs
- (10, 20, 2) has 318 (← 318 ← 403) possible DDs
- (11, 20, 2) has 466 (← 466 ← 546) possible DDs
- (12, 20, 2) has 563 (← 563 ← 752) possible DDs
- (13, 20, 2) has 758 (← 758 ← 1036) possible DDs
- (14, 20, 2) has 962 (← 962 ← 1347) possible DDs
- (15, 20, 2) has 1264 (← 1264 ← 1734) possible DDs
- (16, 20, 2) has 1546 (← 1546 ← 2284) possible DDs
- (17, 20, 2) has 772 (← 772 ← 2862) possible DDs
- (18, 20, 2) has 213 (← 213 ← 3547) possible DDs
- (19, 20, 2) has 52 (← 52 ← 4490) possible DDs
20.40.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 40, 3) has 1 (← 1 ← 1) possible DDs
- (4, 40, 3) has 6 (← 6 ← 6) possible DDs
- (5, 40, 3) has 10 (← 10 ← 12) possible DDs
- (6, 40, 3) has 14 (← 14 ← 28) possible DDs
- (7, 40, 3) has 16 (← 24 ← 54) possible DDs
- (8, 40, 3) has 34 (← 34 ← 106) possible DDs
- (9, 40, 3) has 23 (← 23 ← 177) possible DDs
- (10, 40, 3) has 50 (← 50 ← 286) possible DDs
- (11, 40, 3) has 37 (← 37 ← 415) possible DDs
- (12, 40, 3) has 79 (← 79 ← 644) possible DDs
- (13, 40, 3) has 55 (← 55 ← 895) possible DDs
- (14, 40, 3) has 91 (← 91 ← 1276) possible DDs
- (15, 40, 3) has 80 (← 80 ← 1722) possible DDs
- (16, 40, 3) has 137 (← 137 ← 2417) possible DDs
- (17, 40, 3) has 102 (← 102 ← 3236) possible DDs
- (18, 40, 3) has 58 (← 58 ← 4313) possible DDs
- (19, 40, 3) has 29 (← 29 ← 5607) possible DDs
- (20, 40, 3) has 15 (← 15 ← 7563) possible DDs
Row 12.192.5
9.24.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 24, 2) has 1 (← 1 ← 1) possible DDs
- (3, 24, 2) has 7 (← 7 ← 7) possible DDs
- (4, 24, 2) has 18 (← 18 ← 18) possible DDs
- (5, 24, 2) has 45 (← 45 ← 49) possible DDs
- (6, 24, 2) has 99 (← 99 ← 103) possible DDs
- (7, 24, 2) has 194 (← 194 ← 204) possible DDs
- (8, 24, 2) has 342 (← 342 ← 358) possible DDs
- (9, 24, 2) has 560 (← 560 ← 590) possible DDs
10.48.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 48, 3) has 1 (← 1 ← 1) possible DDs
- (4, 48, 3) has 7 (← 7 ← 7) possible DDs
- (5, 48, 3) has 17 (← 17 ← 17) possible DDs
- (6, 48, 3) has 34 (← 34 ← 44) possible DDs
- (7, 48, 3) has 62 (← 68 ← 94) possible DDs
- (8, 48, 3) has 125 (← 147 ← 206) possible DDs
11.96.4, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (4, 96, 4) has 1 (← 1 ← 1) possible DDs
- (5, 96, 4) has 7 (← 7 ← 7) possible DDs
- (6, 96, 4) has 16 (← 16 ← 16) possible DDs
- (7, 96, 4) has 16 (← 16 ← 32) possible DDs
- (8, 96, 4) has 15 (← 20 ← 75) possible DDs
- (9, 96, 4) has 0 (← 0 ← 134) possible DDs
12.192.5, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (5, 192, 5) has 1 (← 1 ← 1) possible DDs
- (6, 192, 5) has 7 (← 7 ← 7) possible DDs
- (7, 192, 5) has 16 (← 16 ← 16) possible DDs
- (8, 192, 5) has 12 (← 12 ← 33) possible DDs
- (9, 192, 5) has 4 (← 8 ← 67) possible DDs
- (10, 192, 5) has 0 (← 0 ← 120) possible DDs
Row 14.6144.10
6.24.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 24, 2) has 1 (← 1 ← 1) possible DDs
- (3, 24, 2) has 7 (← 7 ← 7) possible DDs
- (4, 24, 2) has 18 (← 18 ← 18) possible DDs
- (5, 24, 2) has 45 (← 45 ← 49) possible DDs
- (6, 24, 2) has 99 (← 99 ← 103) possible DDs
7.48.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 48, 3) has 1 (← 1 ← 1) possible DDs
- (4, 48, 3) has 7 (← 7 ← 7) possible DDs
- (5, 48, 3) has 17 (← 17 ← 17) possible DDs
- (6, 48, 3) has 34 (← 34 ← 44) possible DDs
- (7, 48, 3) has 62 (← 68 ← 94) possible DDs
8.96.4, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (4, 96, 4) has 1 (← 1 ← 1) possible DDs
- (5, 96, 4) has 7 (← 7 ← 7) possible DDs
- (6, 96, 4) has 16 (← 16 ← 16) possible DDs
- (7, 96, 4) has 16 (← 16 ← 32) possible DDs
- (8, 96, 4) has 15 (← 20 ← 75) possible DDs
9.192.5, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (5, 192, 5) has 1 (← 1 ← 1) possible DDs
- (6, 192, 5) has 7 (← 7 ← 7) possible DDs
- (7, 192, 5) has 16 (← 16 ← 16) possible DDs
- (8, 192, 5) has 12 (← 12 ← 33) possible DDs
- (9, 192, 5) has 4 (← 8 ← 67) possible DDs
10.384.6, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (6, 384, 6) has 1 (← 1 ← 1) possible DDs
- (7, 384, 6) has 7 (← 7 ← 7) possible DDs
- (8, 384, 6) has 16 (← 16 ← 16) possible DDs
- (9, 384, 6) has 5 (← 5 ← 28) possible DDs
- (10, 384, 6) has 0 (← 4 ← 53) possible DDs
11.768.7, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (7, 768, 7) has 1 (← 1 ← 1) possible DDs
- (8, 768, 7) has 7 (← 7 ← 7) possible DDs
- (9, 768, 7) has 16 (← 16 ← 16) possible DDs
- (10, 768, 7) has 3 (← 3 ← 28) possible DDs
- (11, 768, 7) has 0 (← 2 ← 51) possible DDs
12.1536.8, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (8, 1536, 8) has 1 (← 1 ← 1) possible DDs
- (9, 1536, 8) has 7 (← 7 ← 7) possible DDs
- (10, 1536, 8) has 16 (← 16 ← 16) possible DDs
- (11, 1536, 8) has 0 (← 0 ← 24) possible DDs
13.3072.9, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (9, 3072, 9) has 1 (← 1 ← 1) possible DDs
- (10, 3072, 9) has 7 (← 7 ← 7) possible DDs
- (11, 3072, 9) has 16 (← 16 ← 16) possible DDs
- (12, 3072, 9) has 0 (← 0 ← 25) possible DDs
14.6144.10, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (10, 6144, 10) has 1 (← 1 ← 1) possible DDs
- (11, 6144, 10) has 7 (← 7 ← 7) possible DDs
- (12, 6144, 10) has 16 (← 16 ← 16) possible DDs
- (13, 6144, 10) has 0 (← 0 ← 20) possible DDs
Row 13.224.5
10.28.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 28, 2) has 1 (← 1 ← 1) possible DDs
- (3, 28, 2) has 8 (← 8 ← 8) possible DDs
- (4, 28, 2) has 21 (← 21 ← 22) possible DDs
- (5, 28, 2) has 65 (← 65 ← 69) possible DDs
- (6, 28, 2) has 158 (← 158 ← 166) possible DDs
- (7, 28, 2) has 332 (← 332 ← 350) possible DDs
- (8, 28, 2) has 646 (← 646 ← 677) possible DDs
- (9, 28, 2) has 1120 (← 1120 ← 1211) possible DDs
- (10, 28, 2) has 1833 (← 1833 ← 1990) possible DDs
11.56.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 56, 3) has 1 (← 1 ← 1) possible DDs
- (4, 56, 3) has 8 (← 8 ← 8) possible DDs
- (5, 56, 3) has 19 (← 19 ← 21) possible DDs
- (6, 56, 3) has 54 (← 54 ← 64) possible DDs
- (7, 56, 3) has 110 (← 112 ← 154) possible DDs
- (8, 56, 3) has 248 (← 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
Row 14.7168.10
6.28.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 28, 2) has 1 (← 1 ← 1) possible DDs
- (3, 28, 2) has 8 (← 8 ← 8) possible DDs
- (4, 28, 2) has 21 (← 21 ← 22) possible DDs
- (5, 28, 2) has 65 (← 65 ← 69) possible DDs
- (6, 28, 2) has 158 (← 158 ← 166) possible DDs
7.56.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 56, 3) has 1 (← 1 ← 1) possible DDs
- (4, 56, 3) has 8 (← 8 ← 8) possible DDs
- (5, 56, 3) has 19 (← 19 ← 21) possible DDs
- (6, 56, 3) has 54 (← 54 ← 64) possible DDs
- (7, 56, 3) has 110 (← 112 ← 154) possible DDs
8.112.4, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (4, 112, 4) has 1 (← 1 ← 1) possible DDs
- (5, 112, 4) has 8 (← 8 ← 8) possible DDs
- (6, 112, 4) has 16 (← 16 ← 20) possible DDs
- (7, 112, 4) has 18 (← 18 ← 48) possible DDs
- (8, 112, 4) has 34 (← 34 ← 117) possible DDs
9.224.5, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (5, 224, 5) has 1 (← 1 ← 1) possible DDs
- (6, 224, 5) has 8 (← 8 ← 8) possible DDs
- (7, 224, 5) has 13 (← 13 ← 19) possible DDs
- (8, 224, 5) has 6 (← 6 ← 48) possible DDs
- (9, 224, 5) has 9 (← 9 ← 110) possible DDs
10.448.6, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (6, 448, 6) has 1 (← 1 ← 1) possible DDs
- (7, 448, 6) has 8 (← 8 ← 8) possible DDs
- (8, 448, 6) has 9 (← 9 ← 18) possible DDs
- (9, 448, 6) has 0 (← 0 ← 41) possible DDs
11.896.7, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (7, 896, 7) has 1 (← 1 ← 1) possible DDs
- (8, 896, 7) has 8 (← 8 ← 8) possible DDs
- (9, 896, 7) has 5 (← 5 ← 17) possible DDs
- (10, 896, 7) has 0 (← 0← 43) possible DDs
Row 14.8192.10
6.32.2, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (2, 32, 2) has 1 (← 1 ← 1) possible DDs
- (3, 32, 2) has 9 (← 9 ← 9) possible DDs
- (4, 32, 2) has 29 (← 29 ← 29) possible DDs
- (5, 32, 2) has 89 (← 89 ← 93) possible DDs
- (6, 32, 2) has 240 (← 240 ← 250) possible DDs
7.64.3, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (3, 64, 3) has 1 (← 1 ← 1) possible DDs
- (4, 64, 3) has 9 (← 9 ← 9) possible DDs
- (5, 64, 3) has 28 (← 28 ← 28) possible DDs
- (6, 64, 3) has 78 (← 78 ← 93) possible DDs
- (7, 64, 3) has 201 (← 205 ← 249) possible DDs
8.128.4, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (4, 128, 4) has 1 (← 1 ← 1) possible DDs
- (5, 128, 4) has 9 (← 9 ← 9) possible DDs
- (6, 128, 4) has 25 (← 25 ← 25) possible DDs
- (7, 128, 4) has 61 (← 61 ← 71) possible DDs
- (8, 128, 4) has 124 (← 128 ← 188) possible DDs
9.256.5, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (5, 256, 5) has 1 (← 1 ← 1) possible DDs
- (6, 256, 5) has 9 (← 9 ← 9) possible DDs
- (7, 256, 5) has 25 (← 25 ← 25) possible DDs
- (8, 256, 5) has 59 (← 59 ← 72) possible DDs
- (9, 256, 5) has 112 (← 114 ← 182) possible DDs
10.512.6, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (6, 512, 6) has 1 (← 1 ← 1) possible DDs
- (7, 512, 6) has 9 (← 9 ← 9) possible DDs
- (8, 512, 6) has 25 (← 25 ← 25) possible DDs
- (9, 512, 6) has 55 (← 55 ← 65) possible DDs
- (10, 512, 6) has 106 (← 106 ← 148) possible DDs
11.1024.7, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (7, 1024, 7) has 1 (← 1 ← 1) possible DDs
- (8, 1024, 7) has 9 (← 9 ← 9) possible DDs
- (9, 1024, 7) has 25 (← 25 ← 25) possible DDs
- (10, 1024, 7) has 55 (← 55 ← 65) possible DDs
- (11, 1024, 7) has 106 (← 106 ← 145) possible DDs
12.2048.8, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (8, 2048, 8) has 1 (← 1 ← 1) possible DDs
- (9, 2048, 8) has 9 (← 9 ← 9) possible DDs
- (10, 2048, 8) has 25 (← 25 ← 25) possible DDs
- (11, 2048, 8) has 55 (← 55 ← 61) possible DDs
- (12, 2048, 8) has 106 (← 106 ← 138) possible DDs
13.4096.9, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (9, 4096, 9) has 1 (← 1 ← 1) possible DDs
- (10, 4096, 9) has 9 (← 9 ← 9) possible DDs
- (11, 4096, 9) has 25 (← 25 ← 25) possible DDs
- (12, 4096, 9) has 55 (← 55 ← 61) possible DDs
- (13, 4096, 9) has 106 (← 106 ← 137) possible DDs
14.8192.10, W = P ∪ Q , (← W_ndda_1 =
P_ndda_1∪ Q_ndda_1 ← all = internal ∪ external)
- (10, 8192, 10) has 1 (← 1 ← 1) possible DDs
- (11, 8192, 10) has 9 (← 9 ← 9) possible DDs
- (12, 8192, 10) has 25 (← 25 ← 25) possible DDs
- (13, 8192, 10) has 55 (← 55 ← 61) possible DDs
- (14, 8192, 10) has 106 (← 106 ← 142) 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 Coding Theory, Albena, Bulgaria,
June 18-24, (2016)
[5] T. Marinova, M. Stoyanova, Nonexistence of (9; 112; 4) and (10; 224; 5) binary orthogonal arrays, Proc. Fifteenth International Work-shop on Algebraic and Combinatorial Coding Theory, Albena, Bulgaria, June 18-24, (2016)
Authors: T. Marinova, M. Stoynova
Last modified: 28.05.2016