Best Known (64−37, 64, s)-Nets in Base 64
(64−37, 64, 257)-Net over F64 — Constructive and digital
Digital (27, 64, 257)-net over F64, using
- 1 times m-reduction [i] based on digital (27, 65, 257)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 20, 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, 45, 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, 20, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(64−37, 64, 288)-Net in Base 64 — Constructive
(27, 64, 288)-net in base 64, using
- t-expansion [i] based on (22, 64, 288)-net in base 64, using
- 27 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
- 27 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(64−37, 64, 425)-Net over F64 — Digital
Digital (27, 64, 425)-net over F64, using
- t-expansion [i] based on digital (26, 64, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
(64−37, 64, 513)-Net in Base 64
(27, 64, 513)-net in base 64, using
- 12 times m-reduction [i] based on (27, 76, 513)-net in base 64, using
- base change [i] based on digital (8, 57, 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, 57, 513)-net over F256, using
(64−37, 64, 251422)-Net in Base 64 — Upper bound on s
There is no (27, 64, 251423)-net in base 64, because
- 1 times m-reduction [i] would yield (27, 63, 251423)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 615675 830340 781334 295675 819822 626679 998629 105796 404467 536133 677870 239884 629127 101273 999710 947250 509077 687172 513865 > 6463 [i]