Best Known (64−28, 64, s)-Nets in Base 256
(64−28, 64, 4683)-Net over F256 — Constructive and digital
Digital (36, 64, 4683)-net over F256, using
- 2561 times duplication [i] based on digital (35, 63, 4683)-net over F256, using
- net defined by OOA [i] based on linear OOA(25663, 4683, F256, 28, 28) (dual of [(4683, 28), 131061, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(25663, 65562, F256, 28) (dual of [65562, 65499, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(18) [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(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(27) ⊂ Ce(18) [i] based on
- OA 14-folding and stacking [i] based on linear OA(25663, 65562, F256, 28) (dual of [65562, 65499, 29]-code), using
- net defined by OOA [i] based on linear OOA(25663, 4683, F256, 28, 28) (dual of [(4683, 28), 131061, 29]-NRT-code), using
(64−28, 64, 32782)-Net over F256 — Digital
Digital (36, 64, 32782)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25664, 32782, F256, 2, 28) (dual of [(32782, 2), 65500, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25664, 65564, F256, 28) (dual of [65564, 65500, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(25664, 65565, F256, 28) (dual of [65565, 65501, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(17) [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(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2569, 29, F256, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,256)), using
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
- Reed–Solomon code RS(247,256) [i]
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
- construction X applied to Ce(27) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(25664, 65565, F256, 28) (dual of [65565, 65501, 29]-code), using
- OOA 2-folding [i] based on linear OA(25664, 65564, F256, 28) (dual of [65564, 65500, 29]-code), using
(64−28, 64, large)-Net in Base 256 — Upper bound on s
There is no (36, 64, large)-net in base 256, because
- 26 times m-reduction [i] would yield (36, 38, large)-net in base 256, but