MinT - Best Known (134−55, 134, s)-Nets in Base 3

Best Known (134−55, 134, s)-Nets in Base 3

(134−55, 134, 80)-Net over F₃ — Constructive and digital

Digital (79, 134, 80)-net over F₃, using

8 times m-reduction [i] based on digital (79, 142, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 71, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(134−55, 134, 124)-Net over F₃ — Digital

Digital (79, 134, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−55, 134, 1197)-Net in Base 3 — Upper bound on s

There is no (79, 134, 1198)-net in base 3, because

1 times m-reduction [i] would yield (79, 133, 1198)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2907 001516 690131 029206 940317 031893 639081 917003 462110 552902 494289 > 3¹³³ [i]