Best Known (57, 57+78, s)-Nets in Base 9
(57, 57+78, 96)-Net over F9 — Constructive and digital
Digital (57, 135, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 44, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (13, 91, 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 (5, 44, 32)-net over F9, using
(57, 57+78, 182)-Net over F9 — Digital
Digital (57, 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
(57, 57+78, 3844)-Net in Base 9 — Upper bound on s
There is no (57, 135, 3845)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 670 715795 379844 918388 198018 002610 887416 370893 845625 273920 442576 517118 347463 810053 971814 812961 366781 194595 326376 248824 867466 992345 > 9135 [i]