Best Known (58, 58+78, s)-Nets in Base 9
(58, 58+78, 98)-Net over F9 — Constructive and digital
Digital (58, 136, 98)-net over F9, using
- (u, u+v)-construction [i] based on
- 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
- net from sequence [i] based on digital (6, 33)-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 (6, 45, 34)-net over F9, using
(58, 58+78, 182)-Net over F9 — Digital
Digital (58, 136, 182)-net over F9, using
- t-expansion [i] based on digital (50, 136, 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
(58, 58+78, 4068)-Net in Base 9 — Upper bound on s
There is no (58, 136, 4069)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 6023 739416 541022 803465 502585 234507 927777 310858 547359 325401 296630 657618 042197 798070 493978 193505 763996 217106 004041 054190 607721 795545 > 9136 [i]