Best Known (18, 18+36, s)-Nets in Base 5
(18, 18+36, 43)-Net over F5 — Constructive and digital
Digital (18, 54, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(18, 18+36, 223)-Net in Base 5 — Upper bound on s
There is no (18, 54, 224)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 58 598023 538737 397690 918333 446908 046849 > 554 [i]