Best Known (162−40, 162, s)-Nets in Base 3
(162−40, 162, 328)-Net over F3 — Constructive and digital
Digital (122, 162, 328)-net over F3, using
- 32 times duplication [i] based on digital (120, 160, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 40, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 40, 82)-net over F81, using
(162−40, 162, 756)-Net over F3 — Digital
Digital (122, 162, 756)-net over F3, using
(162−40, 162, 30386)-Net in Base 3 — Upper bound on s
There is no (122, 162, 30387)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 196699 137685 861343 383580 282886 269922 502368 960208 838443 093906 955216 964096 250809 > 3162 [i]