Best Known (135−76, 135, s)-Nets in Base 9
(135−76, 135, 104)-Net over F9 — Constructive and digital
Digital (59, 135, 104)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 46, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (13, 89, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (8, 46, 40)-net over F9, using
(135−76, 135, 182)-Net over F9 — Digital
Digital (59, 135, 182)-net over F9, using
- t-expansion [i] based on digital (50, 135, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(135−76, 135, 4587)-Net in Base 9 — Upper bound on s
There is no (59, 135, 4588)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 666 630660 643936 221587 509607 009704 523102 963227 212783 811652 416171 912064 230458 634472 468936 714475 556084 014639 143275 178277 970542 528705 > 9135 [i]