Best Known (10, 10+8, s)-Nets in Base 256
(10, 10+8, 16386)-Net over F256 — Constructive and digital
Digital (10, 18, 16386)-net over F256, using
- 2561 times duplication [i] based on digital (9, 17, 16386)-net over F256, using
- net defined by OOA [i] based on linear OOA(25617, 16386, F256, 8, 8) (dual of [(16386, 8), 131071, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(25617, 65544, F256, 8) (dual of [65544, 65527, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- 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(2569, 65536, F256, 5) (dual of [65536, 65527, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(7) ⊂ Ce(4) [i] based on
- OA 4-folding and stacking [i] based on linear OA(25617, 65544, F256, 8) (dual of [65544, 65527, 9]-code), using
- net defined by OOA [i] based on linear OOA(25617, 16386, F256, 8, 8) (dual of [(16386, 8), 131071, 9]-NRT-code), using
(10, 10+8, 65547)-Net over F256 — Digital
Digital (10, 18, 65547)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25618, 65547, F256, 8) (dual of [65547, 65529, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- 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(2567, 65536, F256, 4) (dual of [65536, 65529, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(7) ⊂ Ce(3) [i] based on
(10, 10+8, large)-Net in Base 256 — Upper bound on s
There is no (10, 18, large)-net in base 256, because
- 6 times m-reduction [i] would yield (10, 12, large)-net in base 256, but