Best Known (192, 192+47, s)-Nets in Base 3
(192, 192+47, 692)-Net over F3 — Constructive and digital
Digital (192, 239, 692)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 23, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (169, 216, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 54, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 54, 172)-net over F81, using
- digital (0, 23, 4)-net over F3, using
(192, 192+47, 2734)-Net over F3 — Digital
Digital (192, 239, 2734)-net over F3, using
(192, 192+47, 407915)-Net in Base 3 — Upper bound on s
There is no (192, 239, 407916)-net in base 3, because
- 1 times m-reduction [i] would yield (192, 238, 407916)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 358817 351315 352266 071872 984867 389363 341389 667829 808870 113513 184314 958057 462984 150889 213726 382915 313582 382909 734481 > 3238 [i]