MinT - Best Known (198−86, 198, s)-Nets in Base 3

Best Known (198−86, 198, s)-Nets in Base 3

(198−86, 198, 128)-Net over F₃ — Constructive and digital

Digital (112, 198, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 99, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(198−86, 198, 147)-Net over F₃ — Digital

Digital (112, 198, 147)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−86, 198, 1286)-Net in Base 3 — Upper bound on s

There is no (112, 198, 1287)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29779 048696 145092 172786 024599 457736 424876 050367 666700 691318 652626 576234 764591 565324 073934 389835 > 3¹⁹⁸ [i]