Best Known (108−86, 108, s)-Nets in Base 9
(108−86, 108, 78)-Net over F9 — Constructive and digital
Digital (22, 108, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
(108−86, 108, 88)-Net over F9 — Digital
Digital (22, 108, 88)-net over F9, using
- t-expansion [i] based on digital (21, 108, 88)-net over F9, using
- net from sequence [i] based on digital (21, 87)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 21 and N(F) ≥ 88, using
- net from sequence [i] based on digital (21, 87)-sequence over F9, using
(108−86, 108, 500)-Net in Base 9 — Upper bound on s
There is no (22, 108, 501)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 12 286170 889438 105407 592915 736660 805599 988128 562635 935070 018952 576523 584987 179306 706956 207186 571770 548089 > 9108 [i]