Best Known (73−50, 73, s)-Nets in Base 64
(73−50, 73, 177)-Net over F64 — Constructive and digital
Digital (23, 73, 177)-net over F64, using
- t-expansion [i] based on digital (7, 73, 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
(73−50, 73, 288)-Net in Base 64 — Constructive
(23, 73, 288)-net in base 64, using
- t-expansion [i] based on (22, 73, 288)-net in base 64, using
- 18 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
- 18 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(73−50, 73, 342)-Net over F64 — Digital
Digital (23, 73, 342)-net over F64, using
- t-expansion [i] based on digital (20, 73, 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
(73−50, 73, 30349)-Net in Base 64 — Upper bound on s
There is no (23, 73, 30350)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 710017 405573 341602 775944 072829 721716 825446 417803 177525 149290 163733 191773 855558 598153 764655 830433 217669 329232 968008 804621 275351 476328 > 6473 [i]