MinT - Best Known (118, 118+75, s)-Nets in Base 3

Best Known (118, 118+75, s)-Nets in Base 3

(118, 118+75, 148)-Net over F₃ — Constructive and digital

Digital (118, 193, 148)-net over F₃, using

9 times m-reduction [i] based on digital (118, 202, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 101, 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]

(118, 118+75, 197)-Net over F₃ — Digital

Digital (118, 193, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+75, 2155)-Net in Base 3 — Upper bound on s

There is no (118, 193, 2156)-net in base 3, because

1 times m-reduction [i] would yield (118, 192, 2156)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 953889 899108 778501 496549 814477 641738 634872 008685 635602 264397 924908 826234 711112 991039 061945 > 3¹⁹² [i]