Best Known (58−28, 58, s)-Nets in Base 256
(58−28, 58, 4681)-Net over F256 — Constructive and digital
Digital (30, 58, 4681)-net over F256, using
- 2561 times duplication [i] based on digital (29, 57, 4681)-net over F256, using
- t-expansion [i] based on digital (28, 57, 4681)-net over F256, using
- net defined by OOA [i] based on linear OOA(25657, 4681, F256, 29, 29) (dual of [(4681, 29), 135692, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25657, 65535, F256, 29) (dual of [65535, 65478, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25657, 65535, F256, 29) (dual of [65535, 65478, 30]-code), using
- net defined by OOA [i] based on linear OOA(25657, 4681, F256, 29, 29) (dual of [(4681, 29), 135692, 30]-NRT-code), using
- t-expansion [i] based on digital (28, 57, 4681)-net over F256, using
(58−28, 58, 16386)-Net over F256 — Digital
Digital (30, 58, 16386)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25658, 16386, F256, 4, 28) (dual of [(16386, 4), 65486, 29]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25657, 16386, F256, 4, 28) (dual of [(16386, 4), 65487, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25657, 65544, F256, 28) (dual of [65544, 65487, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(27) ⊂ Ce(24) [i] based on
- OOA 4-folding [i] based on linear OA(25657, 65544, F256, 28) (dual of [65544, 65487, 29]-code), using
- 2561 times duplication [i] based on linear OOA(25657, 16386, F256, 4, 28) (dual of [(16386, 4), 65487, 29]-NRT-code), using
(58−28, 58, large)-Net in Base 256 — Upper bound on s
There is no (30, 58, large)-net in base 256, because
- 26 times m-reduction [i] would yield (30, 32, large)-net in base 256, but