Best Known (49−38, 49, s)-Nets in Base 64
(49−38, 49, 177)-Net over F64 — Constructive and digital
Digital (11, 49, 177)-net over F64, using
- t-expansion [i] based on digital (7, 49, 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
(49−38, 49, 192)-Net in Base 64 — Constructive
(11, 49, 192)-net in base 64, using
- 7 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 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, 48, 192)-net over F128, using
(49−38, 49, 225)-Net over F64 — Digital
Digital (11, 49, 225)-net over F64, using
- t-expansion [i] based on digital (10, 49, 225)-net over F64, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 10 and N(F) ≥ 225, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
(49−38, 49, 5717)-Net in Base 64 — Upper bound on s
There is no (11, 49, 5718)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 31872 956780 095361 419858 203978 927085 379027 924905 768434 053727 858985 245950 406806 763013 028662 > 6449 [i]