Best Known (37, 37+19, s)-Nets in Base 256
(37, 37+19, 932066)-Net over F256 — Constructive and digital
Digital (37, 56, 932066)-net over F256, using
- 2561 times duplication [i] based on digital (36, 55, 932066)-net over F256, using
- net defined by OOA [i] based on linear OOA(25655, 932066, F256, 19, 19) (dual of [(932066, 19), 17709199, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25655, 8388595, F256, 19) (dual of [8388595, 8388540, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25655, 8388595, F256, 19) (dual of [8388595, 8388540, 20]-code), using
- net defined by OOA [i] based on linear OOA(25655, 932066, F256, 19, 19) (dual of [(932066, 19), 17709199, 20]-NRT-code), using
(37, 37+19, 3579378)-Net over F256 — Digital
Digital (37, 56, 3579378)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25656, 3579378, F256, 2, 19) (dual of [(3579378, 2), 7158700, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25656, 4194301, F256, 2, 19) (dual of [(4194301, 2), 8388546, 20]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25655, 4194301, F256, 2, 19) (dual of [(4194301, 2), 8388547, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25655, 8388602, F256, 19) (dual of [8388602, 8388547, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- OOA 2-folding [i] based on linear OA(25655, 8388602, F256, 19) (dual of [8388602, 8388547, 20]-code), using
- 2561 times duplication [i] based on linear OOA(25655, 4194301, F256, 2, 19) (dual of [(4194301, 2), 8388547, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25656, 4194301, F256, 2, 19) (dual of [(4194301, 2), 8388546, 20]-NRT-code), using
(37, 37+19, large)-Net in Base 256 — Upper bound on s
There is no (37, 56, large)-net in base 256, because
- 17 times m-reduction [i] would yield (37, 39, large)-net in base 256, but