Best Known (37−31, 37, s)-Nets in Base 9
(37−31, 37, 34)-Net over F9 — Constructive and digital
Digital (6, 37, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
(37−31, 37, 35)-Net over F9 — Digital
Digital (6, 37, 35)-net over F9, using
- net from sequence [i] based on digital (6, 34)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 35, using
(37−31, 37, 145)-Net in Base 9 — Upper bound on s
There is no (6, 37, 146)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(937, 146, S9, 31), but
- the linear programming bound shows that M ≥ 228 107249 823359 650616 637949 308455 852684 621653 954148 776396 828502 867325 / 1098 181387 948739 739837 582258 823021 > 937 [i]