Best Known (56, 56+56, s)-Nets in Base 9
(56, 56+56, 164)-Net over F9 — Constructive and digital
Digital (56, 112, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 56, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(56, 56+56, 217)-Net over F9 — Digital
Digital (56, 112, 217)-net over F9, using
(56, 56+56, 9248)-Net in Base 9 — Upper bound on s
There is no (56, 112, 9249)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 75050 045046 029823 880740 762120 789342 881669 802833 898977 882221 286713 444852 915446 179704 208943 809921 913002 720097 > 9112 [i]