Best Known (25, 25+53, s)-Nets in Base 64
(25, 25+53, 177)-Net over F64 — Constructive and digital
Digital (25, 78, 177)-net over F64, using
- t-expansion [i] based on digital (7, 78, 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+53, 288)-Net in Base 64 — Constructive
(25, 78, 288)-net in base 64, using
- t-expansion [i] based on (22, 78, 288)-net in base 64, using
- 13 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
- 13 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(25, 25+53, 408)-Net over F64 — Digital
Digital (25, 78, 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+53, 37400)-Net in Base 64 — Upper bound on s
There is no (25, 78, 37401)-net in base 64, because
- 1 times m-reduction [i] would yield (25, 77, 37401)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 11 915062 685710 329067 487303 968446 390765 408009 492309 242054 818469 853649 969421 333371 770590 851935 099874 512011 939025 463469 615382 225310 504469 494528 > 6477 [i]