MinT - Best Known (67−22, 67, s)-Nets in Base 9

Best Known (67−22, 67, s)-Nets in Base 9

(67−22, 67, 344)-Net over F₉ — Constructive and digital

Digital (45, 67, 344)-net over F₉, using

9 times m-reduction [i] based on digital (45, 76, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 38, 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]

(67−22, 67, 1212)-Net over F₉ — Digital

Digital (45, 67, 1212)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67−22, 67, 398218)-Net in Base 9 — Upper bound on s

There is no (45, 67, 398219)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8595 128371 695964 014553 071266 607351 330900 627485 463788 363308 105545 > 9⁶⁷ [i]