MinT - Best Known (239−92, 239, s)-Nets in Base 3

Best Known (239−92, 239, s)-Nets in Base 3

(239−92, 239, 156)-Net over F₃ — Constructive and digital

Digital (147, 239, 156)-net over F₃, using

11 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 125, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(239−92, 239, 243)-Net over F₃ — Digital

Digital (147, 239, 243)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−92, 239, 2665)-Net in Base 3 — Upper bound on s

There is no (147, 239, 2666)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 076776 244911 624715 831919 416480 514026 225145 194378 735117 584505 613463 445597 753849 664717 079639 151925 207080 922876 006845 > 3²³⁹ [i]