Best Known (7, 7+34, s)-Nets in Base 9
(7, 7+34, 36)-Net over F9 — Constructive and digital
Digital (7, 41, 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+34, 40)-Net over F9 — Digital
Digital (7, 41, 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+34, 165)-Net in Base 9 — Upper bound on s
There is no (7, 41, 166)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(941, 166, S9, 34), but
- the linear programming bound shows that M ≥ 828 367269 822422 951530 891556 803019 188245 440510 720863 642985 279256 496500 000000 / 606980 457072 619459 488412 727226 558199 > 941 [i]