Best Known (18−13, 18, s)-Nets in Base 5
(18−13, 18, 20)-Net over F5 — Constructive and digital
Digital (5, 18, 20)-net over F5, using
- net from sequence [i] based on digital (5, 19)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 5 and N(F) ≥ 20, using
(18−13, 18, 67)-Net in Base 5 — Upper bound on s
There is no (5, 18, 68)-net in base 5, because
- 1 times m-reduction [i] would yield (5, 17, 68)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 787029 688001 > 517 [i]