Best Known (75−48, 75, s)-Nets in Base 64
(75−48, 75, 177)-Net over F64 — Constructive and digital
Digital (27, 75, 177)-net over F64, using
- t-expansion [i] based on digital (7, 75, 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
(75−48, 75, 288)-Net in Base 64 — Constructive
(27, 75, 288)-net in base 64, using
- t-expansion [i] based on (22, 75, 288)-net in base 64, using
- 16 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
- 16 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(75−48, 75, 425)-Net over F64 — Digital
Digital (27, 75, 425)-net over F64, using
- t-expansion [i] based on digital (26, 75, 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
(75−48, 75, 513)-Net in Base 64
(27, 75, 513)-net in base 64, using
- 1 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
(75−48, 75, 68589)-Net in Base 64 — Upper bound on s
There is no (27, 75, 68590)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2907 582312 668563 079053 959700 017927 500797 919935 173215 675555 629307 053675 770114 990824 317911 820750 514823 389233 731699 773635 365010 253220 011866 > 6475 [i]