MinT - Best Known (141−45, 141, s)-Nets in Base 3

Best Known (141−45, 141, s)-Nets in Base 3

(141−45, 141, 156)-Net over F₃ — Constructive and digital

Digital (96, 141, 156)-net over F₃, using

7 times m-reduction [i] based on digital (96, 148, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 74, 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]

(141−45, 141, 271)-Net over F₃ — Digital

Digital (96, 141, 271)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−45, 141, 4899)-Net in Base 3 — Upper bound on s

There is no (96, 141, 4900)-net in base 3, because

1 times m-reduction [i] would yield (96, 140, 4900)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 280033 827572 141231 565818 349898 183864 713153 954024 685013 805172 466841 > 3¹⁴⁰ [i]