Best Known (45−23, 45, s)-Nets in Base 4
(45−23, 45, 36)-Net over F4 — Constructive and digital
Digital (22, 45, 36)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 15)-net over F4, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- digital (7, 30, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (4, 15, 15)-net over F4, using
(45−23, 45, 44)-Net over F4 — Digital
Digital (22, 45, 44)-net over F4, using
- t-expansion [i] based on digital (21, 45, 44)-net over F4, using
- net from sequence [i] based on digital (21, 43)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 44, using
- net from sequence [i] based on digital (21, 43)-sequence over F4, using
(45−23, 45, 410)-Net in Base 4 — Upper bound on s
There is no (22, 45, 411)-net in base 4, because
- 1 times m-reduction [i] would yield (22, 44, 411)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 315 018607 246512 354779 432932 > 444 [i]