Best Known (64, 64+28, s)-Nets in Base 27
(64, 64+28, 1409)-Net over F27 — Constructive and digital
Digital (64, 92, 1409)-net over F27, using
- net defined by OOA [i] based on linear OOA(2792, 1409, F27, 28, 28) (dual of [(1409, 28), 39360, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2792, 19726, F27, 28) (dual of [19726, 19634, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2792, 19729, F27, 28) (dual of [19729, 19637, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(15) [i] based on
- linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2746, 19683, F27, 16) (dual of [19683, 19637, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2713, 46, F27, 11) (dual of [46, 33, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2713, 48, F27, 11) (dual of [48, 35, 12]-code), using
- extended algebraic-geometric code AGe(F,36P) [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- discarding factors / shortening the dual code based on linear OA(2713, 48, F27, 11) (dual of [48, 35, 12]-code), using
- construction X applied to Ce(27) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(2792, 19729, F27, 28) (dual of [19729, 19637, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2792, 19726, F27, 28) (dual of [19726, 19634, 29]-code), using
(64, 64+28, 31685)-Net over F27 — Digital
Digital (64, 92, 31685)-net over F27, using
(64, 64+28, large)-Net in Base 27 — Upper bound on s
There is no (64, 92, large)-net in base 27, because
- 26 times m-reduction [i] would yield (64, 66, large)-net in base 27, but