MinT - Best Known (134−41, 134, s)-Nets in Base 3

Best Known (134−41, 134, s)-Nets in Base 3

(134−41, 134, 156)-Net over F₃ — Constructive and digital

Digital (93, 134, 156)-net over F₃, using

8 times m-reduction [i] based on digital (93, 142, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 71, 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]

(134−41, 134, 297)-Net over F₃ — Digital

Digital (93, 134, 297)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−41, 134, 6162)-Net in Base 3 — Upper bound on s

There is no (93, 134, 6163)-net in base 3, because

1 times m-reduction [i] would yield (93, 133, 6163)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2868 941546 988026 977843 152071 535063 443098 136140 777746 449989 291449 > 3¹³³ [i]