Best Known (26, 26+25, s)-Nets in Base 256
(26, 26+25, 5461)-Net over F256 — Constructive and digital
Digital (26, 51, 5461)-net over F256, using
- 2562 times duplication [i] based on digital (24, 49, 5461)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 5461, F256, 25, 25) (dual of [(5461, 25), 136476, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25649, 65533, F256, 25) (dual of [65533, 65484, 26]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25649, 65533, F256, 25) (dual of [65533, 65484, 26]-code), using
- net defined by OOA [i] based on linear OOA(25649, 5461, F256, 25, 25) (dual of [(5461, 25), 136476, 26]-NRT-code), using
(26, 26+25, 14855)-Net over F256 — Digital
Digital (26, 51, 14855)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25651, 14855, F256, 4, 25) (dual of [(14855, 4), 59369, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25651, 16386, F256, 4, 25) (dual of [(16386, 4), 65493, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25651, 65544, F256, 25) (dual of [65544, 65493, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- 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(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(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(24) ⊂ Ce(21) [i] based on
- OOA 4-folding [i] based on linear OA(25651, 65544, F256, 25) (dual of [65544, 65493, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(25651, 16386, F256, 4, 25) (dual of [(16386, 4), 65493, 26]-NRT-code), using
(26, 26+25, large)-Net in Base 256 — Upper bound on s
There is no (26, 51, large)-net in base 256, because
- 23 times m-reduction [i] would yield (26, 28, large)-net in base 256, but