Best Known (12, 12+10, s)-Nets in Base 256
(12, 12+10, 13109)-Net over F256 — Constructive and digital
Digital (12, 22, 13109)-net over F256, using
- net defined by OOA [i] based on linear OOA(25622, 13109, F256, 10, 10) (dual of [(13109, 10), 131068, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(25622, 65545, F256, 10) (dual of [65545, 65523, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25622, 65547, F256, 10) (dual of [65547, 65525, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(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(9) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(25622, 65547, F256, 10) (dual of [65547, 65525, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(25622, 65545, F256, 10) (dual of [65545, 65523, 11]-code), using
(12, 12+10, 32773)-Net over F256 — Digital
Digital (12, 22, 32773)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25622, 32773, F256, 2, 10) (dual of [(32773, 2), 65524, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25622, 65546, F256, 10) (dual of [65546, 65524, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25622, 65547, F256, 10) (dual of [65547, 65525, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(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(9) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(25622, 65547, F256, 10) (dual of [65547, 65525, 11]-code), using
- OOA 2-folding [i] based on linear OA(25622, 65546, F256, 10) (dual of [65546, 65524, 11]-code), using
(12, 12+10, large)-Net in Base 256 — Upper bound on s
There is no (12, 22, large)-net in base 256, because
- 8 times m-reduction [i] would yield (12, 14, large)-net in base 256, but