Best Known (55, 55+68, s)-Nets in Base 9
(55, 55+68, 104)-Net over F9 — Constructive and digital
Digital (55, 123, 104)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 42, 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, 81, 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, 42, 40)-net over F9, using
(55, 55+68, 182)-Net over F9 — Digital
Digital (55, 123, 182)-net over F9, using
- t-expansion [i] based on digital (50, 123, 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
(55, 55+68, 4771)-Net in Base 9 — Upper bound on s
There is no (55, 123, 4772)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2369 713397 565449 229192 819738 409960 486131 129373 038526 038171 581489 725357 976707 057979 464880 417486 637644 780622 403678 174401 > 9123 [i]