Best Known (139−132, 139, s)-Nets in Base 9
(139−132, 139, 36)-Net over F9 — Constructive and digital
Digital (7, 139, 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
(139−132, 139, 40)-Net over F9 — Digital
Digital (7, 139, 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
(139−132, 139, 73)-Net in Base 9 — Upper bound on s
There is no (7, 139, 74)-net in base 9, because
- 72 times m-reduction [i] would yield (7, 67, 74)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(967, 74, S9, 60), but
- the linear programming bound shows that M ≥ 985656 408650 624771 763245 030155 475596 055326 621140 743196 169188 696976 053441 / 111 718145 > 967 [i]
- extracting embedded orthogonal array [i] would yield OA(967, 74, S9, 60), but