OA.729.12.3.5


OA(729,12,3,5)
λ = 3, 1 / 44315
d(C) = 6
ρ(C) ≤ 4
After reduction: 1 / 4
d(C) = 6
ρ(C) ≤ 3
↙    ↘
OA(243,11,3,4)
λ = 3, 1 / 8234
d(C) = 6
ρ(C) ≤ 5
OA(486,11,3,4)
λ = 6, 12986 / 252479
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
After reduction: 1 / 6
d(C) = 6
ρ(C) ≤ 5
After reduction: /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
  ↙     ↘   
   ↙     ↘  
OA(81,10,3,3)
λ = 3, 56 / 2458
3 ≤ d(C) ≤ 6
ρ(C) ≤ 5
OA(162,10,3,3)
λ = 6, 14176 / 85431
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
OA(324,10,3,3)
λ = 12, /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
After reduction: 26 / 1454
4 ≤ d(C) ≤ 6
ρ(C) ≤ 5
After reduction: /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
After reduction: /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(27,9,3,2)
λ = 3, 16 / 488
3 ≤ d(C) ≤ 6
ρ(C) ≤ 5
OA(54,9,3,2)
λ = 6, 1806 / 11663
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
OA(108,9,3,2)
λ = 12, 174682 / 489416
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
OA(216,9,3,2)
λ = 24, /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
After reduction: 11 / 416
4 ≤ d(C) ≤ 6
ρ(C) ≤ 5
After reduction: /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
After reduction: /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
After reduction: /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
  ↙    ↘   
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(9,8,3,1)
λ = 3, 141 / 495
1 ≤ d(C) ≤ 6
ρ(C) ≤ 5
OA(18,8,3,1)
λ = 6, 6959 / 14721
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
OA(36,8,3,1)
λ = 12, 503812 / 767228
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
OA(72,8,3,1)
λ = 24, /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5
OA(144,8,3,1)
λ = 48, /
1 ≤ d(C) ≤ 5
ρ(C) ≤ 5


OA(729,11,3,5)
λ = 3, 1 / 11299
d(C) = 5
ρ(C) ≤ 4
After reduction: 1 / 3
d(C) = 5
ρ(C) ≤ 2
↙    ↘
OA(243,10,3,4)
λ = 3, 1 / 2861
d(C) = 5
ρ(C) ≤ 4
OA(486,10,3,4)
λ = 6, 6497 / 59667
1 ≤ d(C) ≤ 4
ρ(C) ≤ 3
After reduction: 1 / 330
d(C) = 5
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
  ↙     ↘   
   ↙     ↘  
OA(81,9,3,3)
λ = 3, 51 / 1068
2 ≤ d(C) ≤ 5
ρ(C) ≤ 4
OA(162,9,3,3)
λ = 6, 5728 / 24903
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(324,9,3,3)
λ = 12, 380199 / 829750
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: 29 / 668
3 ≤ d(C) ≤ 5
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(27,8,3,2)
λ = 3, 19 / 285
2 ≤ d(C) ≤ 5
ρ(C) ≤ 4
OA(54,8,3,2)
λ = 6, 1114 / 4986
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(108,8,3,2)
λ = 12, 60708 / 137897
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(216,8,3,2)
λ = 24, /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: 16 / 243
3 ≤ d(C) ≤ 5
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
  ↙    ↘   
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(9,7,3,1)
λ = 3, 86 / 268
1 ≤ d(C) ≤ 5
ρ(C) ≤ 4
OA(18,7,3,1)
λ = 6, 2742 / 5353
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(36,7,3,1)
λ = 12, 116680 / 168907
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(72,7,3,1)
λ = 24, /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(144,7,3,1)
λ = 48, /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4


OA(729,10,3,5)
λ = 3, 31 / 2853
2 ≤ d(C) ≤ 4
ρ(C) ≤ 3
After reduction: 5 / 506
3 ≤ d(C) ≤ 4
ρ(C) ≤ 3
↙    ↘
OA(243,9,3,4)
λ = 3, 15 / 975
3 ≤ d(C) ≤ 4
ρ(C) ≤ 3
OA(486,9,3,4)
λ = 6, 2914 / 14343
1 ≤ d(C) ≤ 4
ρ(C) ≤ 3
After reduction: 5 / 355
3 ≤ d(C) ≤ 4
ρ(C) ≤ 3
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 3
  ↙     ↘   
   ↙     ↘  
OA(81,8,3,3)
λ = 3, 52 / 443
1 ≤ d(C) ≤ 4
ρ(C) ≤ 3
OA(162,8,3,3)
λ = 6, 2285 / 6714
1 ≤ d(C) ≤ 4
ρ(C) ≤ 3
OA(324,8,3,3)
λ = 12, 76591 / 135116
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: 24 / 254
2 ≤ d(C) ≤ 4
ρ(C) ≤ 3
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 3
After reduction: /
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(27,7,3,2)
λ = 3, 19 / 155
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(54,7,3,2)
λ = 6, 632 / 1924
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(108,7,3,2)
λ = 12, 18800 / 34134
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(216,7,3,2)
λ = 24, 570458 / 779388
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: 14 / 129
2 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
After reduction: /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
  ↙    ↘   
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(9,6,3,1)
λ = 3, 51 / 139
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(18,6,3,1)
λ = 6, 1009 / 1804
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(36,6,3,1)
λ = 12, 24615 / 33800
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(72,6,3,1)
λ = 24, 680202 / 803603
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4
OA(144,6,3,1)
λ = 48, /
1 ≤ d(C) ≤ 4
ρ(C) ≤ 4


OA(729,9,3,5)
λ = 3, 94 / 678
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: 19 / 168
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
↙    ↘
OA(243,8,3,4)
λ = 3, 51 / 334
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(486,8,3,4)
λ = 6, 1234 / 3180
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: 18 / 138
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
  ↙     ↘   
   ↙     ↘  
OA(81,7,3,3)
λ = 3, 32 / 162
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(162,7,3,3)
λ = 6, 635 / 1490
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(324,7,3,3)
λ = 12, 10952 / 17081
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: 18 / 104
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: /
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: /
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(27,6,3,2)
λ = 3, 15 / 75
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(54,6,3,2)
λ = 6, 266 / 616
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(108,6,3,2)
λ = 12, 4201 / 6562
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(216,6,3,2)
λ = 24, 66401 / 83664
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: 13 / 66
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: /
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: /
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
After reduction: /
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
  ↙    ↘   
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(9,5,3,1)
λ = 3, 28 / 66
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(18,5,3,1)
λ = 6, 339 / 553
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(36,5,3,1)
λ = 12, 4651 / 6043
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(72,5,3,1)
λ = 24, 68503 / 78943
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3
OA(144,5,3,1)
λ = 48, 1049890 / 1125475
1 ≤ d(C) ≤ 3
ρ(C) ≤ 3


OA(729,8,3,5)
λ = 3, 39 / 128
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
After reduction: 13 / 50
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
↙    ↘
OA(243,7,3,4)
λ = 3, 27 / 86
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
OA(486,7,3,4)
λ = 6, 272 / 494
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: 15 / 48
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
  ↙     ↘   
   ↙     ↘  
OA(81,6,3,3)
λ = 3, 19 / 56
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
OA(162,6,3,3)
λ = 6, 174 / 312
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(324,6,3,3)
λ = 12, 1503 / 2027
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: 14 / 41
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(27,5,3,2)
λ = 3, 13 / 37
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
OA(54,5,3,2)
λ = 6, 107 / 189
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(108,5,3,2)
λ = 12, 876 / 1177
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(216,5,3,2)
λ = 24, 7076 / 8232
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: 12 / 33
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
  ↙    ↘   
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(9,4,3,1)
λ = 3, 15 / 30
1 ≤ d(C) ≤ 3
ρ(C) ≤ 2
OA(18,4,3,1)
λ = 6, 104 / 153
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(36,4,3,1)
λ = 12, 775 / 950
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(72,4,3,1)
λ = 24, 5978 / 6639
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(144,4,3,1)
λ = 48, 46948 / 49517
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2


OA(729,7,3,5)
λ = 3, 13 / 24
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: 6 / 11
1 ≤ d(C) ≤ 2
ρ(C) = 1
↙    ↘
OA(243,6,3,4)
λ = 3, 12 / 22
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(486,6,3,4)
λ = 6, 51 / 70
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: 6 / 11
1 ≤ d(C) ≤ 2
ρ(C) = 1
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
  ↙     ↘   
   ↙     ↘  
OA(81,5,3,3)
λ = 3, 10 / 18
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(162,5,3,3)
λ = 6, 42 / 58
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(324,5,3,3)
λ = 12, 174 / 205
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: 6 / 11
1 ≤ d(C) ≤ 2
ρ(C) = 1
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
  ↙     ↘   
  ↙     ↘   
   ↙     ↘  
OA(27,4,3,2)
λ = 3, 9 / 16
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(54,4,3,2)
λ = 6, 36 / 49
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(108,4,3,2)
λ = 12, 144 / 169
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(216,4,3,2)
λ = 24, 576 / 625
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: 8 / 13
1 ≤ d(C) ≤ 2
ρ(C) = 1
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
After reduction: /
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
  ↙    ↘   
  ↙    ↘   
  ↙    ↘   
   ↙    ↘  
OA(9,3,3,1)
λ = 3, 7 / 12
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(18,3,3,1)
λ = 6, 27 / 37
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(36,3,3,1)
λ = 12, 108 / 127
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(72,3,3,1)
λ = 24, 432 / 469
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2
OA(144,3,3,1)
λ = 48, 1728 / 1801
1 ≤ d(C) ≤ 2
ρ(C) ≤ 2


OA(729,6,3,5)
λ = 3, 3 / 4
d(C) = 1
ρ(C) = 1
↙    ↘
OA(243,5,3,4)
λ = 3, 3 / 4
d(C) = 1
ρ(C) = 1
OA(486,5,3,4)
λ = 6, 6 / 7
d(C) = 1
ρ(C) = 1
  ↙     ↘   
   ↙     ↘  
OA(81,4,3,3)
λ = 3, 3 / 4
d(C) = 1
ρ(C) = 1
OA(162,4,3,3)
λ = 6, 6 / 7
d(C) = 1
ρ(C) = 1
OA(324,4,3,3)
λ = 12, 12 / 13
d(C) = 1
ρ(C) = 1
  ↙     ↘   
  ↙     ↘   
   ↙     ↘  
OA(27,3,3,2)
λ = 3, 3 / 4
d(C) = 1
ρ(C) = 1
OA(54,3,3,2)
λ = 6, 6 / 7
d(C) = 1
ρ(C) = 1
OA(108,3,3,2)
λ = 12, 12 / 13
d(C) = 1
ρ(C) = 1
OA(216,3,3,2)
λ = 24, 24 / 25
d(C) = 1
ρ(C) = 1
  ↙     ↘   
  ↙     ↘   
  ↙     ↘   
   ↙     ↘  
OA(9,2,3,1)
λ = 3, 3 / 4
d(C) = 1
ρ(C) = 1
OA(18,2,3,1)
λ = 6, 6 / 7
d(C) = 1
ρ(C) = 1
OA(36,2,3,1)
λ = 12, 12 / 13
d(C) = 1
ρ(C) = 1
OA(72,2,3,1)
λ = 24, 24 / 25
d(C) = 1
ρ(C) = 1
OA(144,2,3,1)
λ = 48, 48 / 49
d(C) = 1
ρ(C) = 1


OA(729,5,3,5)
λ = 3, 1 / 1
d(C) = 1
ρ(C) = 0
↙    ↘
OA(243,4,3,4)
λ = 3, 1 / 1
d(C) = 1
ρ(C) = 0
OA(486,4,3,4)
λ = 6, 1 / 1
d(C) = 1
ρ(C) = 0
  ↙     ↘   
   ↙     ↘  
OA(81,3,3,3)
λ = 3, 1 / 1
d(C) = 1
ρ(C) = 0
OA(162,3,3,3)
λ = 6, 1 / 1
d(C) = 1
ρ(C) = 0
OA(324,3,3,3)
λ = 12, 1 / 1
d(C) = 1
ρ(C) = 0
  ↙     ↘   
  ↙     ↘   
   ↙     ↘  
OA(27,2,3,2)
λ = 3, 1 / 1
d(C) = 1
ρ(C) = 0
OA(54,2,3,2)
λ = 6, 1 / 1
d(C) = 1
ρ(C) = 0
OA(108,2,3,2)
λ = 12, 1 / 1
d(C) = 1
ρ(C) = 0
OA(216,2,3,2)
λ = 24, 1 / 1
d(C) = 1
ρ(C) = 0
  ↙     ↘   
  ↙     ↘   
  ↙     ↘   
   ↙     ↘  
OA(9,1,3,1)
λ = 3, 1 / 1
d(C) = 1
ρ(C) = 0
OA(18,1,3,1)
λ = 6, 1 / 1
d(C) = 1
ρ(C) = 0
OA(36,1,3,1)
λ = 12, 1 / 1
d(C) = 1
ρ(C) = 0
OA(72,1,3,1)
λ = 24, 1 / 1
d(C) = 1
ρ(C) = 0
OA(144,1,3,1)
λ = 48, 1 / 1
d(C) = 1
ρ(C) = 0