Best Known (20, 38, s)-Nets in Base 256
(20, 38, 7283)-Net over F256 — Constructive and digital
Digital (20, 38, 7283)-net over F256, using
- net defined by OOA [i] based on linear OOA(25638, 7283, F256, 18, 18) (dual of [(7283, 18), 131056, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25638, 65547, F256, 18) (dual of [65547, 65509, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- 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(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(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- OA 9-folding and stacking [i] based on linear OA(25638, 65547, F256, 18) (dual of [65547, 65509, 19]-code), using
(20, 38, 21849)-Net over F256 — Digital
Digital (20, 38, 21849)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25638, 21849, F256, 3, 18) (dual of [(21849, 3), 65509, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25638, 65547, F256, 18) (dual of [65547, 65509, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- 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(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(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- OOA 3-folding [i] based on linear OA(25638, 65547, F256, 18) (dual of [65547, 65509, 19]-code), using
(20, 38, large)-Net in Base 256 — Upper bound on s
There is no (20, 38, large)-net in base 256, because
- 16 times m-reduction [i] would yield (20, 22, large)-net in base 256, but