MinT - Best Known (173, 173+57, s)-Nets in Base 3

Best Known (173, 173+57, s)-Nets in Base 3

(173, 173+57, 328)-Net over F₃ — Constructive and digital

Digital (173, 230, 328)-net over F₃, using

3² times duplication [i] based on digital (171, 228, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 57, 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]

(173, 173+57, 987)-Net over F₃ — Digital

Digital (173, 230, 987)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173, 173+57, 45069)-Net in Base 3 — Upper bound on s

There is no (173, 230, 45070)-net in base 3, because

1 times m-reduction [i] would yield (173, 229, 45070)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 237539 663864 109973 135119 429427 163718 360113 859087 775465 244093 093705 098796 566839 289625 136652 432512 520653 238137 > 3²²⁹ [i]