Best Known (39−30, 39, s)-Nets in Base 64
(39−30, 39, 177)-Net over F64 — Constructive and digital
Digital (9, 39, 177)-net over F64, using
- t-expansion [i] based on digital (7, 39, 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
(39−30, 39, 192)-Net in Base 64 — Constructive
(9, 39, 192)-net in base 64, using
- 3 times m-reduction [i] based on (9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
(39−30, 39, 209)-Net over F64 — Digital
Digital (9, 39, 209)-net over F64, using
- net from sequence [i] based on digital (9, 208)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 9 and N(F) ≥ 209, using
(39−30, 39, 5056)-Net in Base 64 — Upper bound on s
There is no (9, 39, 5057)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 27625 972045 930833 749923 441766 115108 351112 467796 044270 546011 536843 023808 > 6439 [i]