MinT - Best Known (196−80, 196, s)-Nets in Base 3

Best Known (196−80, 196, s)-Nets in Base 3

(196−80, 196, 148)-Net over F₃ — Constructive and digital

Digital (116, 196, 148)-net over F₃, using

2 times m-reduction [i] based on digital (116, 198, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 99, 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]

(196−80, 196, 173)-Net over F₃ — Digital

Digital (116, 196, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−80, 196, 1677)-Net in Base 3 — Upper bound on s

There is no (116, 196, 1678)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3323 805113 417841 033573 207529 922934 157717 882018 482511 863931 184910 162479 112507 611384 004150 754449 > 3¹⁹⁶ [i]