Best Known (56, 56+73, s)-Nets in Base 9
(56, 56+73, 102)-Net over F9 — Constructive and digital
Digital (56, 129, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 39, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (17, 90, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (3, 39, 28)-net over F9, using
(56, 56+73, 182)-Net over F9 — Digital
Digital (56, 129, 182)-net over F9, using
- t-expansion [i] based on digital (50, 129, 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+73, 4388)-Net in Base 9 — Upper bound on s
There is no (56, 129, 4389)-net in base 9, because
- 1 times m-reduction [i] would yield (56, 128, 4389)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 139 291348 003700 075905 212274 838431 373395 405508 620378 738388 997545 655633 126335 035294 426619 240007 341355 057547 359006 771734 627361 > 9128 [i]