Best Known (29, 51, s)-Nets in Base 256
(29, 51, 5960)-Net over F256 — Constructive and digital
Digital (29, 51, 5960)-net over F256, using
- net defined by OOA [i] based on linear OOA(25651, 5960, F256, 22, 22) (dual of [(5960, 22), 131069, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(25651, 65560, F256, 22) (dual of [65560, 65509, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(25651, 65562, F256, 22) (dual of [65562, 65511, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(12) [i] based on
- 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(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(21) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(25651, 65562, F256, 22) (dual of [65562, 65511, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(25651, 65560, F256, 22) (dual of [65560, 65509, 23]-code), using
(29, 51, 34139)-Net over F256 — Digital
Digital (29, 51, 34139)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25651, 34139, F256, 22) (dual of [34139, 34088, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(25651, 65562, F256, 22) (dual of [65562, 65511, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(12) [i] based on
- 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(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(21) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(25651, 65562, F256, 22) (dual of [65562, 65511, 23]-code), using
(29, 51, large)-Net in Base 256 — Upper bound on s
There is no (29, 51, large)-net in base 256, because
- 20 times m-reduction [i] would yield (29, 31, large)-net in base 256, but