Best Known (107−68, 107, s)-Nets in Base 9
(107−68, 107, 81)-Net over F9 — Constructive and digital
Digital (39, 107, 81)-net over F9, using
- t-expansion [i] based on digital (32, 107, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(107−68, 107, 140)-Net over F9 — Digital
Digital (39, 107, 140)-net over F9, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 39 and N(F) ≥ 140, using
(107−68, 107, 1683)-Net in Base 9 — Upper bound on s
There is no (39, 107, 1684)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 290376 449898 855056 220801 208108 989044 890067 754112 097301 700279 741777 890030 337378 528963 846416 010124 384705 > 9107 [i]