Best Known (51, 51+54, s)-Nets in Base 9
(51, 51+54, 110)-Net over F9 — Constructive and digital
Digital (51, 105, 110)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 34, 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
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- digital (17, 71, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (7, 34, 36)-net over F9, using
(51, 51+54, 182)-Net over F9 — Digital
Digital (51, 105, 182)-net over F9, using
- t-expansion [i] based on digital (50, 105, 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
(51, 51+54, 7002)-Net in Base 9 — Upper bound on s
There is no (51, 105, 7003)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 15721 207987 379769 349546 352450 621246 355411 331546 130384 214182 980118 399739 384202 596987 362719 407272 856137 > 9105 [i]