Best Known (34, 48, s)-Nets in Base 256
(34, 48, 1198629)-Net over F256 — Constructive and digital
Digital (34, 48, 1198629)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- digital (1, 8, 258)-net over F256, using
(34, 48, large)-Net over F256 — Digital
Digital (34, 48, large)-net over F256, using
- t-expansion [i] based on digital (33, 48, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25648, large, F256, 15) (dual of [large, large−48, 16]-code), using
- 5 times code embedding in larger space [i] based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 5 times code embedding in larger space [i] based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25648, large, F256, 15) (dual of [large, large−48, 16]-code), using
(34, 48, large)-Net in Base 256 — Upper bound on s
There is no (34, 48, large)-net in base 256, because
- 12 times m-reduction [i] would yield (34, 36, large)-net in base 256, but