Best Known (114−61, 114, s)-Nets in Base 9
(114−61, 114, 108)-Net over F9 — Constructive and digital
Digital (53, 114, 108)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 36, 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 (17, 78, 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 (6, 36, 34)-net over F9, using
(114−61, 114, 182)-Net over F9 — Digital
Digital (53, 114, 182)-net over F9, using
- t-expansion [i] based on digital (50, 114, 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
(114−61, 114, 5897)-Net in Base 9 — Upper bound on s
There is no (53, 114, 5898)-net in base 9, because
- 1 times m-reduction [i] would yield (53, 113, 5898)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 676703 449830 543982 891324 235411 597131 851747 226461 892242 320234 152340 228119 727433 170359 938636 066870 825847 695009 > 9113 [i]