Best Known (40, 117, s)-Nets in Base 9
(40, 117, 81)-Net over F9 — Constructive and digital
Digital (40, 117, 81)-net over F9, using
- t-expansion [i] based on digital (32, 117, 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, 117, 140)-Net over F9 — Digital
Digital (40, 117, 140)-net over F9, using
- t-expansion [i] based on digital (39, 117, 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, 117, 1513)-Net in Base 9 — Upper bound on s
There is no (40, 117, 1514)-net in base 9, because
- 1 times m-reduction [i] would yield (40, 116, 1514)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 494 408987 191521 419433 164544 757699 745959 096484 506272 805412 538708 094687 936311 611579 746764 173848 172098 218493 971489 > 9116 [i]