Best Known (40, 62, s)-Nets in Base 256
(40, 62, 6729)-Net over F256 — Constructive and digital
Digital (40, 62, 6729)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (8, 19, 771)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- digital (0, 5, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- digital (0, 11, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- digital (0, 3, 257)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (21, 43, 5958)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 5958, F256, 22, 22) (dual of [(5958, 22), 131033, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(25643, 65538, F256, 22) (dual of [65538, 65495, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- OA 11-folding and stacking [i] based on linear OA(25643, 65538, F256, 22) (dual of [65538, 65495, 23]-code), using
- net defined by OOA [i] based on linear OOA(25643, 5958, F256, 22, 22) (dual of [(5958, 22), 131033, 23]-NRT-code), using
- digital (8, 19, 771)-net over F256, using
(40, 62, 438535)-Net over F256 — Digital
Digital (40, 62, 438535)-net over F256, using
(40, 62, large)-Net in Base 256 — Upper bound on s
There is no (40, 62, large)-net in base 256, because
- 20 times m-reduction [i] would yield (40, 42, large)-net in base 256, but