MinT - Best Known (115, 115+69, s)-Nets in Base 3

Best Known (115, 115+69, s)-Nets in Base 3

(115, 115+69, 156)-Net over F₃ — Constructive and digital

Digital (115, 184, 156)-net over F₃, using

2 times m-reduction [i] based on digital (115, 186, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 93, 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]

(115, 115+69, 209)-Net over F₃ — Digital

Digital (115, 184, 209)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+69, 2469)-Net in Base 3 — Upper bound on s

There is no (115, 184, 2470)-net in base 3, because

1 times m-reduction [i] would yield (115, 183, 2470)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2062 419798 874613 085784 006821 403643 417792 463683 821057 629414 304574 449324 174547 055753 604461 > 3¹⁸³ [i]