Best Known (120−70, 120, s)-Nets in Base 9
(120−70, 120, 84)-Net over F9 — Constructive and digital
Digital (50, 120, 84)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 37, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (13, 83, 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 (2, 37, 20)-net over F9, using
(120−70, 120, 94)-Net in Base 9 — Constructive
(50, 120, 94)-net in base 9, using
- base change [i] based on digital (10, 80, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
(120−70, 120, 182)-Net over F9 — Digital
Digital (50, 120, 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
(120−70, 120, 3228)-Net in Base 9 — Upper bound on s
There is no (50, 120, 3229)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 3 246347 859785 957351 436614 565587 216726 031950 605582 394566 006096 553016 195130 418558 229313 345723 726007 738217 152504 962041 > 9120 [i]