MinT - Best Known (142, 142+87, s)-Nets in Base 3

Best Known (142, 142+87, s)-Nets in Base 3

(142, 142+87, 156)-Net over F₃ — Constructive and digital

Digital (142, 229, 156)-net over F₃, using

11 times m-reduction [i] based on digital (142, 240, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 120, 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]

(142, 142+87, 244)-Net over F₃ — Digital

Digital (142, 229, 244)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+87, 2817)-Net in Base 3 — Upper bound on s

There is no (142, 229, 2818)-net in base 3, because

1 times m-reduction [i] would yield (142, 228, 2818)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 143841 413960 261461 850323 642747 854135 535850 069493 728789 581162 652220 497717 345884 088990 026009 870657 222437 671745 > 3²²⁸ [i]