Best Known (45−39, 45, s)-Nets in Base 9
(45−39, 45, 34)-Net over F9 — Constructive and digital
Digital (6, 45, 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
(45−39, 45, 35)-Net over F9 — Digital
Digital (6, 45, 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
(45−39, 45, 122)-Net in Base 9 — Upper bound on s
There is no (6, 45, 123)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(945, 123, S9, 39), but
- the linear programming bound shows that M ≥ 291271 652551 840646 662314 062573 503935 956851 895422 420929 266128 540852 102667 456822 619759 / 31471 126214 656703 221683 262030 854270 155695 > 945 [i]