Best Known (18, 18+63, s)-Nets in Base 5
(18, 18+63, 43)-Net over F5 — Constructive and digital
Digital (18, 81, 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+63, 102)-Net in Base 5 — Upper bound on s
There is no (18, 81, 103)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(581, 103, S5, 63), but
- the linear programming bound shows that M ≥ 66 303804 549821 335919 093076 276416 807990 354840 285363 025031 983852 386474 609375 / 159953 932348 710192 > 581 [i]