MinT - Best Known (91−36, 91, s)-Nets in Base 9

Best Known (91−36, 91, s)-Nets in Base 9

(91−36, 91, 344)-Net over F₉ — Constructive and digital

Digital (55, 91, 344)-net over F₉, using

5 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]

(91−36, 91, 544)-Net over F₉ — Digital

Digital (55, 91, 544)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−36, 91, 62978)-Net in Base 9 — Upper bound on s

There is no (55, 91, 62979)-net in base 9, because

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]