Best Known (13−6, 13, s)-Nets in Base 256
(13−6, 13, 21848)-Net over F256 — Constructive and digital
Digital (7, 13, 21848)-net over F256, using
- net defined by OOA [i] based on linear OOA(25613, 21848, F256, 6, 6) (dual of [(21848, 6), 131075, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25613, 65544, F256, 6) (dual of [65544, 65531, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2565, 65536, F256, 3) (dual of [65536, 65531, 4]-code or 65536-cap in PG(4,256)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(5) ⊂ Ce(2) [i] based on
- OA 3-folding and stacking [i] based on linear OA(25613, 65544, F256, 6) (dual of [65544, 65531, 7]-code), using
(13−6, 13, 65544)-Net over F256 — Digital
Digital (7, 13, 65544)-net over F256, using
- net defined by OOA [i] based on linear OOA(25613, 65544, F256, 6, 6) (dual of [(65544, 6), 393251, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(25613, 65544, F256, 5, 6) (dual of [(65544, 5), 327707, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25613, 65544, F256, 6) (dual of [65544, 65531, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2565, 65536, F256, 3) (dual of [65536, 65531, 4]-code or 65536-cap in PG(4,256)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(5) ⊂ Ce(2) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25613, 65544, F256, 6) (dual of [65544, 65531, 7]-code), using
- appending kth column [i] based on linear OOA(25613, 65544, F256, 5, 6) (dual of [(65544, 5), 327707, 7]-NRT-code), using
(13−6, 13, large)-Net in Base 256 — Upper bound on s
There is no (7, 13, large)-net in base 256, because
- 4 times m-reduction [i] would yield (7, 9, large)-net in base 256, but