Best Known (18, 61, s)-Nets in Base 5
(18, 61, 43)-Net over F5 — Constructive and digital
Digital (18, 61, 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, 61, 194)-Net in Base 5 — Upper bound on s
There is no (18, 61, 195)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(561, 195, S5, 43), but
- the linear programming bound shows that M ≥ 1965 802275 894790 584384 913871 317751 236081 064217 091524 959229 415969 730325 741693 377494 812011 718750 000000 / 435 983831 567644 608384 762635 867806 667450 090857 729940 922851 > 561 [i]