Best Known (27, 27+12, s)-Nets in Base 256
(27, 27+12, 1398100)-Net over F256 — Constructive and digital
Digital (27, 39, 1398100)-net over F256, using
- 2562 times duplication [i] based on digital (25, 37, 1398100)-net over F256, using
- t-expansion [i] based on digital (24, 37, 1398100)-net over F256, using
- net defined by OOA [i] based on linear OOA(25637, 1398100, F256, 13, 13) (dual of [(1398100, 13), 18175263, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25637, 8388601, F256, 13) (dual of [8388601, 8388564, 14]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25637, 8388601, F256, 13) (dual of [8388601, 8388564, 14]-code), using
- net defined by OOA [i] based on linear OOA(25637, 1398100, F256, 13, 13) (dual of [(1398100, 13), 18175263, 14]-NRT-code), using
- t-expansion [i] based on digital (24, 37, 1398100)-net over F256, using
(27, 27+12, large)-Net over F256 — Digital
Digital (27, 39, large)-net over F256, using
- 2561 times duplication [i] based on digital (26, 38, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25638, large, F256, 12) (dual of [large, large−38, 13]-code), using
- 4 times code embedding in larger space [i] 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]
- 4 times code embedding in larger space [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25638, large, F256, 12) (dual of [large, large−38, 13]-code), using
(27, 27+12, large)-Net in Base 256 — Upper bound on s
There is no (27, 39, large)-net in base 256, because
- 10 times m-reduction [i] would yield (27, 29, large)-net in base 256, but