Best Known (50−29, 50, s)-Nets in Base 64
(50−29, 50, 242)-Net over F64 — Constructive and digital
Digital (21, 50, 242)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (7, 36, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (0, 14, 65)-net over F64, using
(50−29, 50, 288)-Net in Base 64 — Constructive
(21, 50, 288)-net in base 64, using
- 34 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 72, 288)-net over F128, using
(50−29, 50, 342)-Net over F64 — Digital
Digital (21, 50, 342)-net over F64, using
- t-expansion [i] based on digital (20, 50, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
(50−29, 50, 513)-Net in Base 64
(21, 50, 513)-net in base 64, using
- 2 times m-reduction [i] based on (21, 52, 513)-net in base 64, using
- base change [i] based on digital (8, 39, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 39, 513)-net over F256, using
(50−29, 50, 201248)-Net in Base 64 — Upper bound on s
There is no (21, 50, 201249)-net in base 64, because
- 1 times m-reduction [i] would yield (21, 49, 201249)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 31829 855096 047865 091711 853487 959159 556217 087653 787767 964235 637383 561897 707502 064156 977744 > 6449 [i]