Best Known (45, 45+73, s)-Nets in Base 3
(45, 45+73, 48)-Net over F3 — Constructive and digital
Digital (45, 118, 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
(45, 45+73, 56)-Net over F3 — Digital
Digital (45, 118, 56)-net over F3, using
- t-expansion [i] based on digital (40, 118, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
(45, 45+73, 220)-Net in Base 3 — Upper bound on s
There is no (45, 118, 221)-net in base 3, because
- 1 times m-reduction [i] would yield (45, 117, 221)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 75 177516 694276 153859 673814 984338 864481 443887 390049 055377 > 3117 [i]