MinT - Best Known (125, 125+77, s)-Nets in Base 3

Best Known (125, 125+77, s)-Nets in Base 3

(125, 125+77, 156)-Net over F₃ — Constructive and digital

Digital (125, 202, 156)-net over F₃, using

4 times m-reduction [i] based on digital (125, 206, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 103, 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]

(125, 125+77, 216)-Net over F₃ — Digital

Digital (125, 202, 216)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+77, 2471)-Net in Base 3 — Upper bound on s

There is no (125, 202, 2472)-net in base 3, because

1 times m-reduction [i] would yield (125, 201, 2472)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 800583 305088 200103 998475 257866 253361 673911 624720 330860 009886 055609 161394 864613 004293 342621 522929 > 3²⁰¹ [i]