MinT - Best Known (75, 75+39, s)-Nets in Base 3

Best Known (75, 75+39, s)-Nets in Base 3

(75, 75+39, 148)-Net over F₃ — Constructive and digital

Digital (75, 114, 148)-net over F₃, using

2 times m-reduction [i] based on digital (75, 116, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 58, 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]

(75, 75+39, 185)-Net over F₃ — Digital

Digital (75, 114, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+39, 2709)-Net in Base 3 — Upper bound on s

There is no (75, 114, 2710)-net in base 3, because

1 times m-reduction [i] would yield (75, 113, 2710)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 825795 110211 961348 280255 178448 321251 607065 965868 465921 > 3¹¹³ [i]