Best Known (68−28, 68, s)-Nets in Base 256
(68−28, 68, 4684)-Net over F256 — Constructive and digital
Digital (40, 68, 4684)-net over F256, using
- net defined by OOA [i] based on linear OOA(25668, 4684, F256, 28, 28) (dual of [(4684, 28), 131084, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(25668, 65576, F256, 28) (dual of [65576, 65508, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(25668, 65577, F256, 28) (dual of [65577, 65509, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(13) [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(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25613, 41, F256, 13) (dual of [41, 28, 14]-code or 41-arc in PG(12,256)), using
- discarding factors / shortening the dual code based on linear OA(25613, 256, F256, 13) (dual of [256, 243, 14]-code or 256-arc in PG(12,256)), using
- Reed–Solomon code RS(243,256) [i]
- discarding factors / shortening the dual code based on linear OA(25613, 256, F256, 13) (dual of [256, 243, 14]-code or 256-arc in PG(12,256)), using
- construction X applied to Ce(27) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(25668, 65577, F256, 28) (dual of [65577, 65509, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(25668, 65576, F256, 28) (dual of [65576, 65508, 29]-code), using
(68−28, 68, 65577)-Net over F256 — Digital
Digital (40, 68, 65577)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25668, 65577, F256, 28) (dual of [65577, 65509, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(13) [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(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25613, 41, F256, 13) (dual of [41, 28, 14]-code or 41-arc in PG(12,256)), using
- discarding factors / shortening the dual code based on linear OA(25613, 256, F256, 13) (dual of [256, 243, 14]-code or 256-arc in PG(12,256)), using
- Reed–Solomon code RS(243,256) [i]
- discarding factors / shortening the dual code based on linear OA(25613, 256, F256, 13) (dual of [256, 243, 14]-code or 256-arc in PG(12,256)), using
- construction X applied to Ce(27) ⊂ Ce(13) [i] based on
(68−28, 68, large)-Net in Base 256 — Upper bound on s
There is no (40, 68, large)-net in base 256, because
- 26 times m-reduction [i] would yield (40, 42, large)-net in base 256, but