Best Known (27, 55, s)-Nets in Base 128
(27, 55, 1170)-Net over F128 — Constructive and digital
Digital (27, 55, 1170)-net over F128, using
- net defined by OOA [i] based on linear OOA(12855, 1170, F128, 28, 28) (dual of [(1170, 28), 32705, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(12855, 16380, F128, 28) (dual of [16380, 16325, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(12855, 16380, F128, 28) (dual of [16380, 16325, 29]-code), using
(27, 55, 3482)-Net over F128 — Digital
Digital (27, 55, 3482)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12855, 3482, F128, 4, 28) (dual of [(3482, 4), 13873, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12855, 4096, F128, 4, 28) (dual of [(4096, 4), 16329, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- OOA 4-folding [i] based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(12855, 4096, F128, 4, 28) (dual of [(4096, 4), 16329, 29]-NRT-code), using
(27, 55, large)-Net in Base 128 — Upper bound on s
There is no (27, 55, large)-net in base 128, because
- 26 times m-reduction [i] would yield (27, 29, large)-net in base 128, but