Best Known (73−48, 73, s)-Nets in Base 64
(73−48, 73, 177)-Net over F64 — Constructive and digital
Digital (25, 73, 177)-net over F64, using
- t-expansion [i] based on digital (7, 73, 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
(73−48, 73, 288)-Net in Base 64 — Constructive
(25, 73, 288)-net in base 64, using
- t-expansion [i] based on (22, 73, 288)-net in base 64, using
- 18 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
- 18 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(73−48, 73, 408)-Net over F64 — Digital
Digital (25, 73, 408)-net over F64, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 25 and N(F) ≥ 408, using
(73−48, 73, 48496)-Net in Base 64 — Upper bound on s
There is no (25, 73, 48497)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 709867 896387 003650 971511 046036 472390 807014 333207 464468 406211 891094 429921 628059 529347 003219 762331 029187 054000 130684 551185 769984 402244 > 6473 [i]