MinT - Best Known (164, 164+54, s)-Nets in Base 3

Best Known (164, 164+54, s)-Nets in Base 3

(164, 164+54, 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]
    - Niederreiterâ€“Xing sequence constructionÂ 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]

(164, 164+54, 946)-Net over F₃ — Digital

Digital (164, 218, 946)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+54, 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 3^mÂ â‰¥ 102 962653 477157 991790 949978 574484 855235 805270 063654 149075 417588 765851 730315 104055 005869 471086 710772 326139 > 3²¹⁸ [i]