Best Known (42, 42+41, s)-Nets in Base 3
(42, 42+41, 44)-Net over F3 — Constructive and digital
Digital (42, 83, 44)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 27, 16)-net over F3, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- digital (15, 56, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (7, 27, 16)-net over F3, using
(42, 42+41, 56)-Net over F3 — Digital
Digital (42, 83, 56)-net over F3, using
- t-expansion [i] based on digital (40, 83, 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, 42+41, 356)-Net in Base 3 — Upper bound on s
There is no (42, 83, 357)-net in base 3, because
- 1 times m-reduction [i] would yield (42, 82, 357)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1381 257764 840728 202259 219045 785010 181137 > 382 [i]