Best Known (53, 116, s)-Nets in Base 9
(53, 116, 106)-Net over F9 — Constructive and digital
Digital (53, 116, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 36, 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 (17, 80, 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 (5, 36, 32)-net over F9, using
(53, 116, 182)-Net over F9 — Digital
Digital (53, 116, 182)-net over F9, using
- t-expansion [i] based on digital (50, 116, 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, 116, 5362)-Net in Base 9 — Upper bound on s
There is no (53, 116, 5363)-net in base 9, because
- 1 times m-reduction [i] would yield (53, 115, 5363)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 54 911171 923391 656490 760572 165150 192290 578247 311870 395184 472034 122248 977249 031076 588904 877138 462922 322751 734505 > 9115 [i]