Best Known (31, 43, s)-Nets in Base 256
(31, 43, 1398614)-Net over F256 — Constructive and digital
Digital (31, 43, 1398614)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 514)-net over F256, using
- net defined by OOA [i] based on linear OOA(2569, 514, F256, 6, 6) (dual of [(514, 6), 3075, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2569, 514, F256, 5, 6) (dual of [(514, 5), 2561, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2563, 257, F256, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;1282,256) [i]
- linear OOA(2566, 257, F256, 5, 6) (dual of [(257, 5), 1279, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;1279,256) [i]
- linear OOA(2563, 257, F256, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2569, 514, F256, 5, 6) (dual of [(514, 5), 2561, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2569, 514, F256, 6, 6) (dual of [(514, 6), 3075, 7]-NRT-code), 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 (3, 9, 514)-net over F256, using
(31, 43, large)-Net over F256 — Digital
Digital (31, 43, large)-net over F256, using
- t-expansion [i] based on digital (30, 43, large)-net over F256, using
- 1 times m-reduction [i] based on digital (30, 44, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25644, large, F256, 14) (dual of [large, large−44, 15]-code), using
- 4 times code embedding in larger space [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]
- 4 times code embedding in larger space [i] based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25644, large, F256, 14) (dual of [large, large−44, 15]-code), using
- 1 times m-reduction [i] based on digital (30, 44, large)-net over F256, using
(31, 43, large)-Net in Base 256 — Upper bound on s
There is no (31, 43, large)-net in base 256, because
- 10 times m-reduction [i] would yield (31, 33, large)-net in base 256, but