Best Known (53, 111, s)-Nets in Base 9
(53, 111, 110)-Net over F9 — Constructive and digital
Digital (53, 111, 110)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 36, 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, 75, 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, 36, 36)-net over F9, using
(53, 111, 182)-Net over F9 — Digital
Digital (53, 111, 182)-net over F9, using
- t-expansion [i] based on digital (50, 111, 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
(53, 111, 6535)-Net in Base 9 — Upper bound on s
There is no (53, 111, 6536)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8337 001088 139733 583102 663792 095169 093475 911195 395817 339127 654696 498998 927203 038278 879711 656010 949425 596737 > 9111 [i]