Best Known (44, 44+41, s)-Nets in Base 3
(44, 44+41, 47)-Net over F3 — Constructive and digital
Digital (44, 85, 47)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (9, 29, 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, 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 (9, 29, 19)-net over F3, using
(44, 44+41, 56)-Net over F3 — Digital
Digital (44, 85, 56)-net over F3, using
- t-expansion [i] based on digital (40, 85, 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
(44, 44+41, 399)-Net in Base 3 — Upper bound on s
There is no (44, 85, 400)-net in base 3, because
- 1 times m-reduction [i] would yield (44, 84, 400)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 12062 671618 713267 344182 141972 768474 874241 > 384 [i]