MinT - Best Known (140, 140+71, s)-Nets in Base 3

Best Known (140, 140+71, s)-Nets in Base 3

(140, 140+71, 162)-Net over F₃ — Constructive and digital

Digital (140, 211, 162)-net over F₃, using

5 times m-reduction [i] based on digital (140, 216, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 108, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(140, 140+71, 324)-Net over F₃ — Digital

Digital (140, 211, 324)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+71, 5035)-Net in Base 3 — Upper bound on s

There is no (140, 211, 5036)-net in base 3, because

1 times m-reduction [i] would yield (140, 210, 5036)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15787 082923 407883 816450 252425 552378 918014 286347 399338 419954 619835 421290 789339 567645 992806 677427 721425 > 3²¹⁰ [i]