Best Known (69, 69+84, s)-Nets in Base 3
(69, 69+84, 48)-Net over F3 — Constructive and digital
Digital (69, 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
(69, 69+84, 82)-Net over F3 — Digital
Digital (69, 153, 82)-net over F3, using
- net from sequence [i] based on digital (69, 81)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 69 and N(F) ≥ 82, using
(69, 69+84, 411)-Net in Base 3 — Upper bound on s
There is no (69, 153, 412)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 10 252697 204266 004106 047071 734390 164170 726021 301771 734017 416964 669206 033865 > 3153 [i]