Best Known (10, 25, s)-Nets in Base 128
(10, 25, 321)-Net over F128 — Constructive and digital
Digital (10, 25, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (3, 18, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (0, 7, 129)-net over F128, using
(10, 25, 341)-Net over F128 — Digital
Digital (10, 25, 341)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12825, 341, F128, 15) (dual of [341, 316, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(12825, 381, F128, 15) (dual of [381, 356, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(12825, 381, F128, 15) (dual of [381, 356, 16]-code), using
(10, 25, 386)-Net in Base 128 — Constructive
(10, 25, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- (3, 18, 257)-net in base 128, using
- 6 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- base change [i] based on digital (0, 21, 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
- base change [i] based on digital (0, 21, 257)-net over F256, using
- 6 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- digital (0, 7, 129)-net over F128, using
(10, 25, 446510)-Net in Base 128 — Upper bound on s
There is no (10, 25, 446511)-net in base 128, because
- 1 times m-reduction [i] would yield (10, 24, 446511)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 374 146293 855704 869131 552783 016326 891200 341350 714808 > 12824 [i]