Best Known (25, 25+62, s)-Nets in Base 64
(25, 25+62, 177)-Net over F64 — Constructive and digital
Digital (25, 87, 177)-net over F64, using
- t-expansion [i] based on digital (7, 87, 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
(25, 25+62, 288)-Net in Base 64 — Constructive
(25, 87, 288)-net in base 64, using
- t-expansion [i] based on (22, 87, 288)-net in base 64, using
- 4 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
- 4 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(25, 25+62, 408)-Net over F64 — Digital
Digital (25, 87, 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
(25, 25+62, 23086)-Net in Base 64 — Upper bound on s
There is no (25, 87, 23087)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 13 739084 278714 585521 589244 506086 993365 739957 437995 320099 318125 457708 932311 654994 282279 071088 641496 515053 343761 050337 746237 944366 159571 552626 725008 314601 573920 > 6487 [i]