Best Known (42−25, 42, s)-Nets in Base 5
(42−25, 42, 42)-Net over F5 — Constructive and digital
Digital (17, 42, 42)-net over F5, using
- net from sequence [i] based on digital (17, 41)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using
(42−25, 42, 314)-Net in Base 5 — Upper bound on s
There is no (17, 42, 315)-net in base 5, because
- 1 times m-reduction [i] would yield (17, 41, 315)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 45873 891852 494420 129747 232081 > 541 [i]