Best Known (40, 125, s)-Nets in Base 9
(40, 125, 81)-Net over F9 — Constructive and digital
Digital (40, 125, 81)-net over F9, using
- t-expansion [i] based on digital (32, 125, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(40, 125, 140)-Net over F9 — Digital
Digital (40, 125, 140)-net over F9, using
- t-expansion [i] based on digital (39, 125, 140)-net over F9, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 39 and N(F) ≥ 140, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
(40, 125, 1329)-Net in Base 9 — Upper bound on s
There is no (40, 125, 1330)-net in base 9, because
- 1 times m-reduction [i] would yield (40, 124, 1330)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 21464 891142 835628 260759 446275 261718 575403 735535 809283 796337 144878 513387 648836 843212 448999 994028 622826 491652 874972 028257 > 9124 [i]