Best Known (20, 20+50, s)-Nets in Base 64
(20, 20+50, 177)-Net over F64 — Constructive and digital
Digital (20, 70, 177)-net over F64, using
- t-expansion [i] based on digital (7, 70, 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
(20, 20+50, 288)-Net in Base 64 — Constructive
(20, 70, 288)-net in base 64, using
- 7 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 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, 66, 288)-net over F128, using
(20, 20+50, 342)-Net over F64 — Digital
Digital (20, 70, 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
(20, 20+50, 18420)-Net in Base 64 — Upper bound on s
There is no (20, 70, 18421)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2 710200 268970 822789 583898 088957 912161 947775 581694 251224 167301 469862 555237 255891 938006 610006 477014 670008 382609 165637 532023 292592 > 6470 [i]