Best Known (57−37, 57, s)-Nets in Base 64
(57−37, 57, 177)-Net over F64 — Constructive and digital
Digital (20, 57, 177)-net over F64, using
- t-expansion [i] based on digital (7, 57, 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
(57−37, 57, 288)-Net in Base 64 — Constructive
(20, 57, 288)-net in base 64, using
- 20 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
(57−37, 57, 342)-Net over F64 — Digital
Digital (20, 57, 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
(57−37, 57, 49881)-Net in Base 64 — Upper bound on s
There is no (20, 57, 49882)-net in base 64, because
- 1 times m-reduction [i] would yield (20, 56, 49882)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 140008 693820 627860 096935 880107 381925 372871 598998 578042 544170 701330 873377 884927 402657 113638 396151 980044 > 6456 [i]