MinT - Best Known (143−51, 143, s)-Nets in Base 3

Best Known (143−51, 143, s)-Nets in Base 3

(143−51, 143, 148)-Net over F₃ — Constructive and digital

Digital (92, 143, 148)-net over F₃, using

7 times m-reduction [i] based on digital (92, 150, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 75, 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]

(143−51, 143, 196)-Net over F₃ — Digital

Digital (92, 143, 196)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−51, 143, 2585)-Net in Base 3 — Upper bound on s

There is no (92, 143, 2586)-net in base 3, because

1 times m-reduction [i] would yield (92, 142, 2586)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 597704 480797 357826 094690 682841 567780 413879 579515 923047 943031 015109 > 3¹⁴² [i]