Best Known (26−12, 26, s)-Nets in Base 256
(26−12, 26, 10924)-Net over F256 — Constructive and digital
Digital (14, 26, 10924)-net over F256, using
- 2561 times duplication [i] based on digital (13, 25, 10924)-net over F256, using
- net defined by OOA [i] based on linear OOA(25625, 10924, F256, 12, 12) (dual of [(10924, 12), 131063, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(25625, 65544, F256, 12) (dual of [65544, 65519, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- OA 6-folding and stacking [i] based on linear OA(25625, 65544, F256, 12) (dual of [65544, 65519, 13]-code), using
- net defined by OOA [i] based on linear OOA(25625, 10924, F256, 12, 12) (dual of [(10924, 12), 131063, 13]-NRT-code), using
(26−12, 26, 32773)-Net over F256 — Digital
Digital (14, 26, 32773)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25626, 32773, F256, 2, 12) (dual of [(32773, 2), 65520, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25626, 65546, F256, 12) (dual of [65546, 65520, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25626, 65547, F256, 12) (dual of [65547, 65521, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(25626, 65547, F256, 12) (dual of [65547, 65521, 13]-code), using
- OOA 2-folding [i] based on linear OA(25626, 65546, F256, 12) (dual of [65546, 65520, 13]-code), using
(26−12, 26, large)-Net in Base 256 — Upper bound on s
There is no (14, 26, large)-net in base 256, because
- 10 times m-reduction [i] would yield (14, 16, large)-net in base 256, but