Best Known (55−35, 55, s)-Nets in Base 64
(55−35, 55, 177)-Net over F64 — Constructive and digital
Digital (20, 55, 177)-net over F64, using
- t-expansion [i] based on digital (7, 55, 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
(55−35, 55, 288)-Net in Base 64 — Constructive
(20, 55, 288)-net in base 64, using
- 22 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
(55−35, 55, 342)-Net over F64 — Digital
Digital (20, 55, 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
(55−35, 55, 62204)-Net in Base 64 — Upper bound on s
There is no (20, 55, 62205)-net in base 64, because
- 1 times m-reduction [i] would yield (20, 54, 62205)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 34 176868 848749 302569 336270 390823 627081 413847 744074 578305 962962 044229 153603 805995 994451 057934 544244 > 6454 [i]