Best Known (28, 57, s)-Nets in Base 128
(28, 57, 1170)-Net over F128 — Constructive and digital
Digital (28, 57, 1170)-net over F128, using
- net defined by OOA [i] based on linear OOA(12857, 1170, F128, 29, 29) (dual of [(1170, 29), 33873, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12857, 16381, F128, 29) (dual of [16381, 16324, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12857, 16381, F128, 29) (dual of [16381, 16324, 30]-code), using
(28, 57, 3464)-Net over F128 — Digital
Digital (28, 57, 3464)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12857, 3464, F128, 4, 29) (dual of [(3464, 4), 13799, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12857, 4096, F128, 4, 29) (dual of [(4096, 4), 16327, 30]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- OOA 4-folding [i] based on linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using
- discarding factors / shortening the dual code based on linear OOA(12857, 4096, F128, 4, 29) (dual of [(4096, 4), 16327, 30]-NRT-code), using
(28, 57, large)-Net in Base 128 — Upper bound on s
There is no (28, 57, large)-net in base 128, because
- 27 times m-reduction [i] would yield (28, 30, large)-net in base 128, but