Best Known (20, 46, s)-Nets in Base 64
(20, 46, 242)-Net over F64 — Constructive and digital
Digital (20, 46, 242)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 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, 33, 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, 13, 65)-net over F64, using
(20, 46, 288)-Net in Base 64 — Constructive
(20, 46, 288)-net in base 64, using
- 31 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 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, 66, 288)-net over F128, using
(20, 46, 353)-Net over F64 — Digital
Digital (20, 46, 353)-net over F64, using
(20, 46, 513)-Net in Base 64
(20, 46, 513)-net in base 64, using
- 2 times m-reduction [i] based on (20, 48, 513)-net in base 64, using
- base change [i] based on digital (8, 36, 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, 36, 513)-net over F256, using
(20, 46, 221386)-Net in Base 64 — Upper bound on s
There is no (20, 46, 221387)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 121417 866093 171920 360298 251233 374223 235970 528947 007082 113589 238212 736997 655216 662304 > 6446 [i]