Best Known (43, 82, s)-Nets in Base 3
(43, 82, 47)-Net over F3 — Constructive and digital
Digital (43, 82, 47)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (9, 28, 19)-net over F3, using
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
- digital (15, 54, 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 (9, 28, 19)-net over F3, using
(43, 82, 56)-Net over F3 — Digital
Digital (43, 82, 56)-net over F3, using
- t-expansion [i] based on digital (40, 82, 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
(43, 82, 410)-Net in Base 3 — Upper bound on s
There is no (43, 82, 411)-net in base 3, because
- 1 times m-reduction [i] would yield (43, 81, 411)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 451 342546 951196 808162 330685 277589 892971 > 381 [i]