Best Known (7, 7+55, s)-Nets in Base 9
(7, 7+55, 36)-Net over F9 — Constructive and digital
Digital (7, 62, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
(7, 7+55, 40)-Net over F9 — Digital
Digital (7, 62, 40)-net over F9, using
- net from sequence [i] based on digital (7, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 40, using
(7, 7+55, 85)-Net in Base 9 — Upper bound on s
There is no (7, 62, 86)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(962, 86, S9, 55), but
- the linear programming bound shows that M ≥ 154826 646321 157929 341732 607215 889862 829091 783130 008732 097847 275246 876310 057595 / 994876 967088 308171 > 962 [i]