Best Known (117−66, 117, s)-Nets in Base 9
(117−66, 117, 96)-Net over F9 — Constructive and digital
Digital (51, 117, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 38, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (13, 79, 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 (5, 38, 32)-net over F9, using
(117−66, 117, 182)-Net over F9 — Digital
Digital (51, 117, 182)-net over F9, using
- t-expansion [i] based on digital (50, 117, 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
(117−66, 117, 3956)-Net in Base 9 — Upper bound on s
There is no (51, 117, 3957)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4456 159235 864815 460142 989254 891611 539797 268052 623792 208997 439843 130050 817507 704200 851013 549884 556816 862675 938473 > 9117 [i]