Best Known (25, 63, s)-Nets in Base 128
(25, 63, 384)-Net over F128 — Constructive and digital
Digital (25, 63, 384)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 22, 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 (3, 41, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128 (see above)
- digital (3, 22, 192)-net over F128, using
(25, 63, 386)-Net in Base 128 — Constructive
(25, 63, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 19, 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
- (6, 44, 257)-net in base 128, using
- 4 times m-reduction [i] based on (6, 48, 257)-net in base 128, using
- base change [i] based on digital (0, 42, 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, 42, 257)-net over F256, using
- 4 times m-reduction [i] based on (6, 48, 257)-net in base 128, using
- digital (0, 19, 129)-net over F128, using
(25, 63, 513)-Net over F128 — Digital
Digital (25, 63, 513)-net over F128, using
- t-expansion [i] based on digital (24, 63, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
(25, 63, 605996)-Net in Base 128 — Upper bound on s
There is no (25, 63, 605997)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 5 678578 991559 836662 346329 721921 442561 921942 195295 460949 308465 195384 328075 148148 810636 943253 477978 944525 872966 608288 721996 320559 405512 > 12863 [i]