MinT - Best Known (143, 143+107, s)-Nets in Base 3

Best Known (143, 143+107, s)-Nets in Base 3

(143, 143+107, 148)-Net over F₃ — Constructive and digital

Digital (143, 250, 148)-net over F₃, using

t-expansion [i] based on digital (142, 250, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 125, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(143, 143+107, 188)-Net over F₃ — Digital

Digital (143, 250, 188)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+107, 1744)-Net in Base 3 — Upper bound on s

There is no (143, 250, 1745)-net in base 3, because

1 times m-reduction [i] would yield (143, 249, 1745)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65020 780517 733877 446187 191233 555029 152377 122482 801459 572139 378229 856002 902113 117308 048527 544207 091748 340921 855651 539411 > 3²⁴⁹ [i]