Best Known (218−54, 218, s)-Nets in Base 3
(218−54, 218, 328)-Net over F3 — Constructive and digital
Digital (164, 218, 328)-net over F3, using
- 32 times duplication [i] based on digital (162, 216, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 54, 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, 54, 82)-net over F81, using
(218−54, 218, 946)-Net over F3 — Digital
Digital (164, 218, 946)-net over F3, using
(218−54, 218, 38850)-Net in Base 3 — Upper bound on s
There is no (164, 218, 38851)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 102 962653 477157 991790 949978 574484 855235 805270 063654 149075 417588 765851 730315 104055 005869 471086 710772 326139 > 3218 [i]