MinT - Best Known (134−55, 134, s)-Nets in Base 9

Best Known (134−55, 134, s)-Nets in Base 9

(134−55, 134, 344)-Net over F₉ — Constructive and digital

Digital (79, 134, 344)-net over F₉, using

10 times m-reduction [i] based on digital (79, 144, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 72, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(134−55, 134, 612)-Net over F₉ — Digital

Digital (79, 134, 612)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−55, 134, 68507)-Net in Base 9 — Upper bound on s

There is no (79, 134, 68508)-net in base 9, because

1 times m-reduction [i] would yield (79, 133, 68508)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 208501 889233 637592 319276 983619 301600 587489 926333 161948 834521 997423 687983 878875 233651 045528 144391 070881 047641 550364 773092 376097 > 9¹³³ [i]