Best Known (33, 33+56, s)-Nets in Base 9
(33, 33+56, 81)-Net over F9 — Constructive and digital
Digital (33, 89, 81)-net over F9, using
- t-expansion [i] based on digital (32, 89, 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
(33, 33+56, 128)-Net over F9 — Digital
Digital (33, 89, 128)-net over F9, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
(33, 33+56, 1507)-Net in Base 9 — Upper bound on s
There is no (33, 89, 1508)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8 580010 787322 628718 139799 077699 375287 205489 159742 599097 886247 319340 812107 868599 525505 > 989 [i]