Best Known (87−64, 87, s)-Nets in Base 64
(87−64, 87, 177)-Net over F64 — Constructive and digital
Digital (23, 87, 177)-net over F64, using
- t-expansion [i] based on digital (7, 87, 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
(87−64, 87, 288)-Net in Base 64 — Constructive
(23, 87, 288)-net in base 64, using
- t-expansion [i] based on (22, 87, 288)-net in base 64, using
- 4 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
- 4 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(87−64, 87, 342)-Net over F64 — Digital
Digital (23, 87, 342)-net over F64, using
- t-expansion [i] based on digital (20, 87, 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
(87−64, 87, 16507)-Net in Base 64 — Upper bound on s
There is no (23, 87, 16508)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 13 753584 364778 154989 351299 371075 310631 315262 917210 829078 699367 825736 198701 509776 724337 334004 182926 254963 568315 071908 389231 028837 397041 129453 166670 588953 024589 > 6487 [i]