Best Known (24, 62, s)-Nets in Base 64
(24, 62, 193)-Net over F64 — Constructive and digital
Digital (24, 62, 193)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 19, 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 (5, 43, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- digital (0, 19, 65)-net over F64, using
(24, 62, 288)-Net in Base 64 — Constructive
(24, 62, 288)-net in base 64, using
- t-expansion [i] based on (22, 62, 288)-net in base 64, using
- 29 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
- 29 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(24, 62, 342)-Net over F64 — Digital
Digital (24, 62, 342)-net over F64, using
- t-expansion [i] based on digital (20, 62, 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
(24, 62, 513)-Net in Base 64
(24, 62, 513)-net in base 64, using
- 2 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
(24, 62, 98556)-Net in Base 64 — Upper bound on s
There is no (24, 62, 98557)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 9620 919185 579083 416460 433357 206762 486547 879028 185210 326813 076070 167834 428131 368062 473492 851098 104119 568633 486532 > 6462 [i]