MinT - Best Known (140, 140+39, s)-Nets in Base 3

Best Known (140, 140+39, s)-Nets in Base 3

(140, 140+39, 640)-Net over F₃ — Constructive and digital

Digital (140, 179, 640)-net over F₃, using

1 times m-reduction [i] based on digital (140, 180, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 45, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(140, 140+39, 1347)-Net over F₃ — Digital

Digital (140, 179, 1347)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+39, 116947)-Net in Base 3 — Upper bound on s

There is no (140, 179, 116948)-net in base 3, because

1 times m-reduction [i] would yield (140, 178, 116948)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 465324 464009 867383 339552 873799 905804 469617 135878 660793 963850 032763 569297 295199 138289 > 3¹⁷⁸ [i]