Best Known (27, 27+13, s)-Nets in Base 256
(27, 27+13, 1398100)-Net over F256 — Constructive and digital
Digital (27, 40, 1398100)-net over F256, using
- 2563 times duplication [i] based on digital (24, 37, 1398100)-net over F256, using
- net defined by OOA [i] based on linear OOA(25637, 1398100, F256, 13, 13) (dual of [(1398100, 13), 18175263, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25637, 8388601, F256, 13) (dual of [8388601, 8388564, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25637, 8388601, F256, 13) (dual of [8388601, 8388564, 14]-code), using
- net defined by OOA [i] based on linear OOA(25637, 1398100, F256, 13, 13) (dual of [(1398100, 13), 18175263, 14]-NRT-code), using
(27, 27+13, 6649347)-Net over F256 — Digital
Digital (27, 40, 6649347)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25640, 6649347, F256, 13) (dual of [6649347, 6649307, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 13) (dual of [large, large−40, 14]-code), using
- strength reduction [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- strength reduction [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 13) (dual of [large, large−40, 14]-code), using
(27, 27+13, large)-Net in Base 256 — Upper bound on s
There is no (27, 40, large)-net in base 256, because
- 11 times m-reduction [i] would yield (27, 29, large)-net in base 256, but