Best Known (115−63, 115, s)-Nets in Base 9
(115−63, 115, 104)-Net over F9 — Constructive and digital
Digital (52, 115, 104)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 39, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (13, 76, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (8, 39, 40)-net over F9, using
(115−63, 115, 182)-Net over F9 — Digital
Digital (52, 115, 182)-net over F9, using
- t-expansion [i] based on digital (50, 115, 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
(115−63, 115, 4994)-Net in Base 9 — Upper bound on s
There is no (52, 115, 4995)-net in base 9, because
- 1 times m-reduction [i] would yield (52, 114, 4995)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 6 110687 093380 115842 050798 028888 251945 134975 827478 896046 066503 733216 875248 779837 914760 355511 350509 255688 670313 > 9114 [i]