Best Known (65−58, 65, s)-Nets in Base 9
(65−58, 65, 36)-Net over F9 — Constructive and digital
Digital (7, 65, 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
(65−58, 65, 40)-Net over F9 — Digital
Digital (7, 65, 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
(65−58, 65, 74)-Net in Base 9 — Upper bound on s
There is no (7, 65, 75)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(965, 75, S9, 58), but
- the linear programming bound shows that M ≥ 9194 385609 187547 917382 908043 398611 078466 117225 351467 455611 567465 680939 / 76 340336 > 965 [i]