Best Known (42, 105, s)-Nets in Base 3
(42, 105, 42)-Net over F3 — Constructive and digital
Digital (42, 105, 42)-net over F3, using
- t-expansion [i] based on digital (39, 105, 42)-net over F3, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 39 and N(F) ≥ 42, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
(42, 105, 56)-Net over F3 — Digital
Digital (42, 105, 56)-net over F3, using
- t-expansion [i] based on digital (40, 105, 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
(42, 105, 218)-Net in Base 3 — Upper bound on s
There is no (42, 105, 219)-net in base 3, because
- 1 times m-reduction [i] would yield (42, 104, 219)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 44 318162 001021 395177 532517 800964 081808 169373 068339 > 3104 [i]