MinT - Best Known (175, 175+48, s)-Nets in Base 3

Best Known (175, 175+48, s)-Nets in Base 3

(175, 175+48, 688)-Net over F₃ — Constructive and digital

Digital (175, 223, 688)-net over F₃, using

1 times m-reduction [i] based on digital (175, 224, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 56, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(175, 175+48, 1709)-Net over F₃ — Digital

Digital (175, 223, 1709)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+48, 132894)-Net in Base 3 — Upper bound on s

There is no (175, 223, 132895)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25007 164288 473322 571949 156177 616109 375062 404085 159789 587886 940835 371467 200006 116764 405991 291043 746706 767313 > 3²²³ [i]