Best Known (30, 30+17, s)-Nets in Base 256
(30, 30+17, 8963)-Net over F256 — Constructive and digital
Digital (30, 47, 8963)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 771)-net over F256, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 257)-net over F256, using
- digital (0, 4, 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, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- generalized (u, u+v)-construction [i] based on
- digital (16, 33, 8192)-net over F256, using
- net defined by OOA [i] based on linear OOA(25633, 8192, F256, 17, 17) (dual of [(8192, 17), 139231, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- net defined by OOA [i] based on linear OOA(25633, 8192, F256, 17, 17) (dual of [(8192, 17), 139231, 18]-NRT-code), using
- digital (6, 14, 771)-net over F256, using
(30, 30+17, 316384)-Net over F256 — Digital
Digital (30, 47, 316384)-net over F256, using
(30, 30+17, large)-Net in Base 256 — Upper bound on s
There is no (30, 47, large)-net in base 256, because
- 15 times m-reduction [i] would yield (30, 32, large)-net in base 256, but