MinT - Best Known (144, 239, s)-Nets in Base 3

Best Known (144, 239, s)-Nets in Base 3

(144, 239, 156)-Net over F₃ — Constructive and digital

Digital (144, 239, 156)-net over F₃, using

5 times m-reduction [i] based on digital (144, 244, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 122, 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]

(144, 239, 222)-Net over F₃ — Digital

Digital (144, 239, 222)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 239, 2347)-Net in Base 3 — Upper bound on s

There is no (144, 239, 2348)-net in base 3, because

1 times m-reduction [i] would yield (144, 238, 2348)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 359468 404793 964999 698309 144793 926383 836483 239295 595354 782919 743367 868958 931688 453256 289870 577364 703143 854696 916753 > 3²³⁸ [i]