Best Known (18, 85, s)-Nets in Base 5
(18, 85, 43)-Net over F5 — Constructive and digital
Digital (18, 85, 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, 85, 98)-Net in Base 5 — Upper bound on s
There is no (18, 85, 99)-net in base 5, because
- 1 times m-reduction [i] would yield (18, 84, 99)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(584, 99, S5, 66), but
- the linear programming bound shows that M ≥ 1519 347286 873244 313576 059223 193370 772975 185900 577344 000339 508056 640625 / 21630 442609 > 584 [i]
- extracting embedded orthogonal array [i] would yield OA(584, 99, S5, 66), but