MinT - Best Known (192−71, 192, s)-Nets in Base 3

Best Known (192−71, 192, s)-Nets in Base 3

(192−71, 192, 156)-Net over F₃ — Constructive and digital

Digital (121, 192, 156)-net over F₃, using

6 times m-reduction [i] based on digital (121, 198, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 99, 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]

(192−71, 192, 226)-Net over F₃ — Digital

Digital (121, 192, 226)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−71, 192, 2757)-Net in Base 3 — Upper bound on s

There is no (121, 192, 2758)-net in base 3, because

1 times m-reduction [i] would yield (121, 191, 2758)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 508775 413232 245645 817706 493462 641477 279672 571079 797601 075059 090177 005292 197052 860724 557473 > 3¹⁹¹ [i]