Best Known (18, 18+47, s)-Nets in Base 5
(18, 18+47, 43)-Net over F5 — Constructive and digital
Digital (18, 65, 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+47, 176)-Net in Base 5 — Upper bound on s
There is no (18, 65, 177)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(565, 177, S5, 47), but
- the linear programming bound shows that M ≥ 928862 805139 227491 294373 113656 833179 429075 661053 130266 116462 170412 294586 786577 570616 451660 079349 039733 642712 235450 744628 906250 / 326 420638 733071 937644 601839 010375 705679 643066 787569 448457 098518 444348 392763 358711 > 565 [i]