Best Known (57, 57+74, s)-Nets in Base 9
(57, 57+74, 102)-Net over F9 — Constructive and digital
Digital (57, 131, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 40, 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, 91, 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, 40, 28)-net over F9, using
(57, 57+74, 182)-Net over F9 — Digital
Digital (57, 131, 182)-net over F9, using
- t-expansion [i] based on digital (50, 131, 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
(57, 57+74, 4356)-Net in Base 9 — Upper bound on s
There is no (57, 131, 4357)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 102007 701201 863587 394876 524308 956750 321345 994308 263683 676044 295747 737928 711739 778607 657236 381483 223759 720348 792568 412197 464905 > 9131 [i]