Best Known (64−19, 64, s)-Nets in Base 256
(64−19, 64, 932323)-Net over F256 — Constructive and digital
Digital (45, 64, 932323)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (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
- digital (0, 9, 257)-net over F256, using
(64−19, 64, large)-Net over F256 — Digital
Digital (45, 64, large)-net over F256, using
- 1 times m-reduction [i] based on digital (45, 65, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25665, large, F256, 20) (dual of [large, large−65, 21]-code), using
- 7 times code embedding in larger space [i] based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 7 times code embedding in larger space [i] based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25665, large, F256, 20) (dual of [large, large−65, 21]-code), using
(64−19, 64, large)-Net in Base 256 — Upper bound on s
There is no (45, 64, large)-net in base 256, because
- 17 times m-reduction [i] would yield (45, 47, large)-net in base 256, but