MinT - Best Known (168−60, 168, s)-Nets in Base 3

Best Known (168−60, 168, s)-Nets in Base 3

(168−60, 168, 156)-Net over F₃ — Constructive and digital

Digital (108, 168, 156)-net over F₃, using

4 times m-reduction [i] based on digital (108, 172, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 86, 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]

(168−60, 168, 223)-Net over F₃ — Digital

Digital (108, 168, 223)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−60, 168, 2799)-Net in Base 3 — Upper bound on s

There is no (108, 168, 2800)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 860737 769772 676483 441299 377102 626273 689081 841591 841880 309777 360621 588909 392545 > 3¹⁶⁸ [i]