Best Known (37, 63, s)-Nets in Base 256
(37, 63, 5044)-Net over F256 — Constructive and digital
Digital (37, 63, 5044)-net over F256, using
- net defined by OOA [i] based on linear OOA(25663, 5044, F256, 26, 26) (dual of [(5044, 26), 131081, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25663, 65572, F256, 26) (dual of [65572, 65509, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25663, 65574, F256, 26) (dual of [65574, 65511, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(12) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(25612, 38, F256, 12) (dual of [38, 26, 13]-code or 38-arc in PG(11,256)), using
- discarding factors / shortening the dual code based on linear OA(25612, 256, F256, 12) (dual of [256, 244, 13]-code or 256-arc in PG(11,256)), using
- Reed–Solomon code RS(244,256) [i]
- discarding factors / shortening the dual code based on linear OA(25612, 256, F256, 12) (dual of [256, 244, 13]-code or 256-arc in PG(11,256)), using
- construction X applied to Ce(25) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(25663, 65574, F256, 26) (dual of [65574, 65511, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(25663, 65572, F256, 26) (dual of [65572, 65509, 27]-code), using
(37, 63, 63978)-Net over F256 — Digital
Digital (37, 63, 63978)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25663, 63978, F256, 26) (dual of [63978, 63915, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25663, 65574, F256, 26) (dual of [65574, 65511, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(12) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(25612, 38, F256, 12) (dual of [38, 26, 13]-code or 38-arc in PG(11,256)), using
- discarding factors / shortening the dual code based on linear OA(25612, 256, F256, 12) (dual of [256, 244, 13]-code or 256-arc in PG(11,256)), using
- Reed–Solomon code RS(244,256) [i]
- discarding factors / shortening the dual code based on linear OA(25612, 256, F256, 12) (dual of [256, 244, 13]-code or 256-arc in PG(11,256)), using
- construction X applied to Ce(25) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(25663, 65574, F256, 26) (dual of [65574, 65511, 27]-code), using
(37, 63, large)-Net in Base 256 — Upper bound on s
There is no (37, 63, large)-net in base 256, because
- 24 times m-reduction [i] would yield (37, 39, large)-net in base 256, but