Best Known (44, 44+99, s)-Nets in Base 5
(44, 44+99, 78)-Net over F5 — Constructive and digital
Digital (44, 143, 78)-net over F5, using
- t-expansion [i] based on digital (38, 143, 78)-net over F5, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
(44, 44+99, 84)-Net over F5 — Digital
Digital (44, 143, 84)-net over F5, using
- t-expansion [i] based on digital (43, 143, 84)-net over F5, using
- net from sequence [i] based on digital (43, 83)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 43 and N(F) ≥ 84, using
- net from sequence [i] based on digital (43, 83)-sequence over F5, using
(44, 44+99, 471)-Net in Base 5 — Upper bound on s
There is no (44, 143, 472)-net in base 5, because
- 1 times m-reduction [i] would yield (44, 142, 472)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1893 786578 450495 422726 648054 911757 094433 701789 201570 251664 333696 573856 748601 544184 156229 354831 299425 > 5142 [i]