Best Known (18, 18+39, s)-Nets in Base 5
(18, 18+39, 43)-Net over F5 — Constructive and digital
Digital (18, 57, 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+39, 214)-Net in Base 5 — Upper bound on s
There is no (18, 57, 215)-net in base 5, because
- 1 times m-reduction [i] would yield (18, 56, 215)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1483 855704 739818 888330 334574 043389 610645 > 556 [i]