Best Known (48, 68, s)-Nets in Base 256
(48, 68, 839117)-Net over F256 — Constructive and digital
Digital (48, 68, 839117)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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 (38, 58, 838860)-net over F256, using
- net defined by OOA [i] based on linear OOA(25658, 838860, F256, 20, 20) (dual of [(838860, 20), 16777142, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(25658, 8388600, F256, 20) (dual of [8388600, 8388542, 21]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(25658, 8388600, F256, 20) (dual of [8388600, 8388542, 21]-code), using
- net defined by OOA [i] based on linear OOA(25658, 838860, F256, 20, 20) (dual of [(838860, 20), 16777142, 21]-NRT-code), using
- digital (0, 10, 257)-net over F256, using
(48, 68, large)-Net over F256 — Digital
Digital (48, 68, large)-net over F256, using
- t-expansion [i] based on digital (47, 68, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25668, large, F256, 21) (dual of [large, large−68, 22]-code), using
- 7 times code embedding in larger space [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 7 times code embedding in larger space [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25668, large, F256, 21) (dual of [large, large−68, 22]-code), using
(48, 68, large)-Net in Base 256 — Upper bound on s
There is no (48, 68, large)-net in base 256, because
- 18 times m-reduction [i] would yield (48, 50, large)-net in base 256, but