Best Known (64−40, 64, s)-Nets in Base 64
(64−40, 64, 184)-Net over F64 — Constructive and digital
Digital (24, 64, 184)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 21, 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 (3, 43, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- digital (1, 21, 80)-net over F64, using
(64−40, 64, 288)-Net in Base 64 — Constructive
(24, 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
(64−40, 64, 342)-Net over F64 — Digital
Digital (24, 64, 342)-net over F64, using
- t-expansion [i] based on digital (20, 64, 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
(64−40, 64, 513)-Net in Base 64
(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
(64−40, 64, 79375)-Net in Base 64 — Upper bound on s
There is no (24, 64, 79376)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 39 404404 553452 141021 696936 814379 008324 069143 471494 530639 758372 174566 999451 884523 441805 662732 678202 412118 408000 228576 > 6464 [i]