Best Known (50−24, 50, s)-Nets in Base 256
(50−24, 50, 5462)-Net over F256 — Constructive and digital
Digital (26, 50, 5462)-net over F256, using
- 2561 times duplication [i] based on digital (25, 49, 5462)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 5462, F256, 24, 24) (dual of [(5462, 24), 131039, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(23) ⊂ Ce(20) [i] based on
- OA 12-folding and stacking [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- net defined by OOA [i] based on linear OOA(25649, 5462, F256, 24, 24) (dual of [(5462, 24), 131039, 25]-NRT-code), using
(50−24, 50, 16386)-Net over F256 — Digital
Digital (26, 50, 16386)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25650, 16386, F256, 4, 24) (dual of [(16386, 4), 65494, 25]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25649, 16386, F256, 4, 24) (dual of [(16386, 4), 65495, 25]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(23) ⊂ Ce(20) [i] based on
- OOA 4-folding [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- 2561 times duplication [i] based on linear OOA(25649, 16386, F256, 4, 24) (dual of [(16386, 4), 65495, 25]-NRT-code), using
(50−24, 50, large)-Net in Base 256 — Upper bound on s
There is no (26, 50, large)-net in base 256, because
- 22 times m-reduction [i] would yield (26, 28, large)-net in base 256, but