Best Known (54, 54+73, s)-Nets in Base 9
(54, 54+73, 96)-Net over F9 — Constructive and digital
Digital (54, 127, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 41, 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, 86, 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, 41, 32)-net over F9, using
(54, 54+73, 182)-Net over F9 — Digital
Digital (54, 127, 182)-net over F9, using
- t-expansion [i] based on digital (50, 127, 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
(54, 54+73, 3881)-Net in Base 9 — Upper bound on s
There is no (54, 127, 3882)-net in base 9, because
- 1 times m-reduction [i] would yield (54, 126, 3882)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1 717558 749266 688124 736723 861495 470965 583705 835704 851510 878051 430881 292434 436748 911141 805778 839421 926186 737382 930976 501185 > 9126 [i]