MinT - Best Known (92−37, 92, s)-Nets in Base 9

Best Known (92−37, 92, s)-Nets in Base 9

(92−37, 92, 344)-Net over F₉ — Constructive and digital

Digital (55, 92, 344)-net over F₉, using

4 times m-reduction [i] based on digital (55, 96, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 48, 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]

(92−37, 92, 508)-Net over F₉ — Digital

Digital (55, 92, 508)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−37, 92, 62978)-Net in Base 9 — Upper bound on s

There is no (55, 92, 62979)-net in base 9, because

1 times m-reduction [i] would yield (55, 91, 62979)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685 703870 646967 287647 341902 536595 582456 796280 667299 601830 165620 107540 207055 429866 424113 > 9⁹¹ [i]