Best Known (28, 28+12, s)-Nets in Base 256
(28, 28+12, 1398357)-Net over F256 — Constructive and digital
Digital (28, 40, 1398357)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- digital (22, 34, 1398100)-net over F256, using
- net defined by OOA [i] based on linear OOA(25634, 1398100, F256, 12, 12) (dual of [(1398100, 12), 16777166, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- net defined by OOA [i] based on linear OOA(25634, 1398100, F256, 12, 12) (dual of [(1398100, 12), 16777166, 13]-NRT-code), using
- digital (0, 6, 257)-net over F256, using
(28, 28+12, large)-Net over F256 — Digital
Digital (28, 40, large)-net over F256, using
- 1 times m-reduction [i] based on digital (28, 41, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25641, large, F256, 13) (dual of [large, large−41, 14]-code), using
- 4 times code embedding in larger space [i] 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]
- 4 times code embedding in larger space [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25641, large, F256, 13) (dual of [large, large−41, 14]-code), using
(28, 28+12, large)-Net in Base 256 — Upper bound on s
There is no (28, 40, large)-net in base 256, because
- 10 times m-reduction [i] would yield (28, 30, large)-net in base 256, but