MinT - Best Known (181−69, 181, s)-Nets in Base 3

Best Known (181−69, 181, s)-Nets in Base 3

(181−69, 181, 148)-Net over F₃ — Constructive and digital

Digital (112, 181, 148)-net over F₃, using

9 times m-reduction [i] based on digital (112, 190, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 95, 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]

(181−69, 181, 197)-Net over F₃ — Digital

Digital (112, 181, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−69, 181, 2238)-Net in Base 3 — Upper bound on s

There is no (112, 181, 2239)-net in base 3, because

1 times m-reduction [i] would yield (112, 180, 2239)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 675724 257156 697309 246114 264950 815596 112085 977735 618514 378606 874117 386463 251368 300861 > 3¹⁸⁰ [i]