Best Known (56, 56+71, s)-Nets in Base 9
(56, 56+71, 104)-Net over F9 — Constructive and digital
Digital (56, 127, 104)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 43, 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, 84, 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, 43, 40)-net over F9, using
(56, 56+71, 182)-Net over F9 — Digital
Digital (56, 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
(56, 56+71, 4715)-Net in Base 9 — Upper bound on s
There is no (56, 127, 4716)-net in base 9, because
- 1 times m-reduction [i] would yield (56, 126, 4716)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1 728413 231820 647842 523308 677272 185606 492452 714638 892837 305371 675228 592861 105699 691946 949696 192107 003605 563000 604858 717345 > 9126 [i]