Best Known (51−26, 51, s)-Nets in Base 256
(51−26, 51, 5041)-Net over F256 — Constructive and digital
Digital (25, 51, 5041)-net over F256, using
- net defined by OOA [i] based on linear OOA(25651, 5041, F256, 26, 26) (dual of [(5041, 26), 131015, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25651, 65533, F256, 26) (dual of [65533, 65482, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(25651, 65533, F256, 26) (dual of [65533, 65482, 27]-code), using
(51−26, 51, 11256)-Net over F256 — Digital
Digital (25, 51, 11256)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25651, 11256, F256, 5, 26) (dual of [(11256, 5), 56229, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25651, 13107, F256, 5, 26) (dual of [(13107, 5), 65484, 27]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25651, 65535, F256, 26) (dual of [65535, 65484, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- OOA 5-folding [i] based on linear OA(25651, 65535, F256, 26) (dual of [65535, 65484, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(25651, 13107, F256, 5, 26) (dual of [(13107, 5), 65484, 27]-NRT-code), using
(51−26, 51, large)-Net in Base 256 — Upper bound on s
There is no (25, 51, large)-net in base 256, because
- 24 times m-reduction [i] would yield (25, 27, large)-net in base 256, but