Best Known (34, 34+57, s)-Nets in Base 5
(34, 34+57, 72)-Net over F5 — Constructive and digital
Digital (34, 91, 72)-net over F5, using
- t-expansion [i] based on digital (31, 91, 72)-net over F5, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
(34, 34+57, 76)-Net over F5 — Digital
Digital (34, 91, 76)-net over F5, using
- net from sequence [i] based on digital (34, 75)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 34 and N(F) ≥ 76, using
(34, 34+57, 478)-Net in Base 5 — Upper bound on s
There is no (34, 91, 479)-net in base 5, because
- 1 times m-reduction [i] would yield (34, 90, 479)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 842 022204 453870 397401 336945 801823 721580 639306 431645 048706 646929 > 590 [i]