Best Known (40, 40+54, s)-Nets in Base 9
(40, 40+54, 81)-Net over F9 — Constructive and digital
Digital (40, 94, 81)-net over F9, using
- t-expansion [i] based on digital (32, 94, 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, 40+54, 84)-Net in Base 9 — Constructive
(40, 94, 84)-net in base 9, using
- 2 times m-reduction [i] based on (40, 96, 84)-net in base 9, using
- base change [i] based on digital (8, 64, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- base change [i] based on digital (8, 64, 84)-net over F27, using
(40, 40+54, 140)-Net over F9 — Digital
Digital (40, 94, 140)-net over F9, using
- t-expansion [i] based on digital (39, 94, 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, 40+54, 2851)-Net in Base 9 — Upper bound on s
There is no (40, 94, 2852)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 504084 804307 543320 889140 080905 031698 148857 146322 545826 095531 995017 770641 993473 595384 313825 > 994 [i]