MinT - Best Known (141−47, 141, s)-Nets in Base 3

Best Known (141−47, 141, s)-Nets in Base 3

(141−47, 141, 156)-Net over F₃ — Constructive and digital

Digital (94, 141, 156)-net over F₃, using

3 times m-reduction [i] based on digital (94, 144, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 72, 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]

(141−47, 141, 238)-Net over F₃ — Digital

Digital (94, 141, 238)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−47, 141, 3758)-Net in Base 3 — Upper bound on s

There is no (94, 141, 3759)-net in base 3, because

1 times m-reduction [i] would yield (94, 140, 3759)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 270792 814353 267112 943113 528900 634240 704233 766046 596586 177008 059795 > 3¹⁴⁰ [i]