MinT - Best Known (92, 92+42, s)-Nets in Base 3

Best Known (92, 92+42, s)-Nets in Base 3

(92, 92+42, 156)-Net over F₃ — Constructive and digital

Digital (92, 134, 156)-net over F₃, using

6 times m-reduction [i] based on digital (92, 140, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 70, 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]

(92, 92+42, 275)-Net over F₃ — Digital

Digital (92, 134, 275)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 92+42, 4787)-Net in Base 3 — Upper bound on s

There is no (92, 134, 4788)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8618 244905 599739 692503 029317 882417 493333 364362 755551 892988 241993 > 3¹³⁴ [i]