Best Known (57−33, 57, s)-Nets in Base 64
(57−33, 57, 257)-Net over F64 — Constructive and digital
Digital (24, 57, 257)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 17, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (7, 40, 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 (1, 17, 80)-net over F64, using
(57−33, 57, 288)-Net in Base 64 — Constructive
(24, 57, 288)-net in base 64, using
- t-expansion [i] based on (22, 57, 288)-net in base 64, using
- 34 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 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, 78, 288)-net over F128, using
- 34 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(57−33, 57, 348)-Net over F64 — Digital
Digital (24, 57, 348)-net over F64, using
(57−33, 57, 513)-Net in Base 64
(24, 57, 513)-net in base 64, using
- 7 times m-reduction [i] based on (24, 64, 513)-net in base 64, using
- base change [i] based on digital (8, 48, 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, 48, 513)-net over F256, using
(57−33, 57, 226367)-Net in Base 64 — Upper bound on s
There is no (24, 57, 226368)-net in base 64, because
- 1 times m-reduction [i] would yield (24, 56, 226368)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 139993 461590 624498 698292 743899 643359 975289 526174 601833 900357 049159 863496 974253 189585 375112 911039 140245 > 6456 [i]