Best Known (107−55, 107, s)-Nets in Base 5
(107−55, 107, 82)-Net over F5 — Constructive and digital
Digital (52, 107, 82)-net over F5, using
- t-expansion [i] based on digital (48, 107, 82)-net over F5, using
- net from sequence [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- net from sequence [i] based on digital (48, 81)-sequence over F5, using
(107−55, 107, 104)-Net over F5 — Digital
Digital (52, 107, 104)-net over F5, using
- t-expansion [i] based on digital (51, 107, 104)-net over F5, using
- net from sequence [i] based on digital (51, 103)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 51 and N(F) ≥ 104, using
- net from sequence [i] based on digital (51, 103)-sequence over F5, using
(107−55, 107, 1495)-Net in Base 5 — Upper bound on s
There is no (52, 107, 1496)-net in base 5, because
- 1 times m-reduction [i] would yield (52, 106, 1496)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 124 414618 638130 148706 580887 748385 151745 205295 800079 329861 170316 580975 776865 > 5106 [i]