MinT - Best Known (37−17, 37, s)-Nets in Base 9

Best Known (37−17, 37, s)-Nets in Base 9

(37−17, 37, 200)-Net over F₉ — Constructive and digital

Digital (20, 37, 200)-net over F₉, using

1 times m-reduction [i] based on digital (20, 38, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 19, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(37−17, 37, 9257)-Net in Base 9 — Upper bound on s

There is no (20, 37, 9258)-net in base 9, because

1 times m-reduction [i] would yield (20, 36, 9258)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22543 683298 155607 163802 972486 310785 > 9³⁶ [i]