Best Known (23, 23+49, s)-Nets in Base 64
(23, 23+49, 177)-Net over F64 — Constructive and digital
Digital (23, 72, 177)-net over F64, using
- t-expansion [i] based on digital (7, 72, 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
(23, 23+49, 288)-Net in Base 64 — Constructive
(23, 72, 288)-net in base 64, using
- t-expansion [i] based on (22, 72, 288)-net in base 64, using
- 19 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
- 19 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(23, 23+49, 342)-Net over F64 — Digital
Digital (23, 72, 342)-net over F64, using
- t-expansion [i] based on digital (20, 72, 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
(23, 23+49, 34288)-Net in Base 64 — Upper bound on s
There is no (23, 72, 34289)-net in base 64, because
- 1 times m-reduction [i] would yield (23, 71, 34289)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 173 298117 875643 986528 510339 390472 349212 901377 986771 875501 958797 210339 107835 033552 646288 270091 785934 273695 701666 894795 011679 090324 > 6471 [i]