Best Known (78−52, 78, s)-Nets in Base 64
(78−52, 78, 177)-Net over F64 — Constructive and digital
Digital (26, 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
(78−52, 78, 288)-Net in Base 64 — Constructive
(26, 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
(78−52, 78, 425)-Net over F64 — Digital
Digital (26, 78, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
(78−52, 78, 43889)-Net in Base 64 — Upper bound on s
There is no (26, 78, 43890)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 762 187372 341027 587911 518409 551903 667024 426186 253016 815857 785159 262409 846546 631003 934332 805642 955629 471437 404696 497511 379820 850398 345030 438384 > 6478 [i]