Best Known (28, 54, s)-Nets in Base 256
(28, 54, 5042)-Net over F256 — Constructive and digital
Digital (28, 54, 5042)-net over F256, using
- net defined by OOA [i] based on linear OOA(25654, 5042, F256, 26, 26) (dual of [(5042, 26), 131038, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25654, 65546, F256, 26) (dual of [65546, 65492, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] 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]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(25654, 65546, F256, 26) (dual of [65546, 65492, 27]-code), using
(28, 54, 16386)-Net over F256 — Digital
Digital (28, 54, 16386)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25654, 16386, F256, 4, 26) (dual of [(16386, 4), 65490, 27]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25653, 16386, F256, 4, 26) (dual of [(16386, 4), 65491, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25653, 65544, F256, 26) (dual of [65544, 65491, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] 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]
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(25) ⊂ Ce(22) [i] based on
- OOA 4-folding [i] based on linear OA(25653, 65544, F256, 26) (dual of [65544, 65491, 27]-code), using
- 2561 times duplication [i] based on linear OOA(25653, 16386, F256, 4, 26) (dual of [(16386, 4), 65491, 27]-NRT-code), using
(28, 54, large)-Net in Base 256 — Upper bound on s
There is no (28, 54, large)-net in base 256, because
- 24 times m-reduction [i] would yield (28, 30, large)-net in base 256, but