Best Known (67, 67+86, s)-Nets in Base 3
(67, 67+86, 48)-Net over F3 — Constructive and digital
Digital (67, 153, 48)-net over F3, using
- t-expansion [i] based on digital (45, 153, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(67, 67+86, 72)-Net over F3 — Digital
Digital (67, 153, 72)-net over F3, using
- net from sequence [i] based on digital (67, 71)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 67 and N(F) ≥ 72, using
(67, 67+86, 380)-Net in Base 3 — Upper bound on s
There is no (67, 153, 381)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 041294 557568 851860 882326 751959 309177 551173 994050 223531 042601 102359 886251 > 3153 [i]