Best Known (90−69, 90, s)-Nets in Base 5
(90−69, 90, 43)-Net over F5 — Constructive and digital
Digital (21, 90, 43)-net over F5, using
- t-expansion [i] based on digital (18, 90, 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]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(90−69, 90, 50)-Net over F5 — Digital
Digital (21, 90, 50)-net over F5, using
- net from sequence [i] based on digital (21, 49)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 21 and N(F) ≥ 50, using
(90−69, 90, 124)-Net in Base 5 — Upper bound on s
There is no (21, 90, 125)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(590, 125, S5, 69), but
- the linear programming bound shows that M ≥ 2 952328 436639 751682 852727 946353 751062 109766 771925 933068 025649 230747 831097 687594 592571 258544 921875 / 3167 515657 014446 686686 926801 664051 > 590 [i]