MinT - Best Known (16, 31, s)-Nets in Base 9

Best Known (16, 31, s)-Nets in Base 9

(16, 31, 164)-Net over F₉ — Constructive and digital

Digital (16, 31, 164)-net over F₉, using

1 times m-reduction [i] based on digital (16, 32, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 16, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(16, 31, 5189)-Net in Base 9 — Upper bound on s

There is no (16, 31, 5190)-net in base 9, because

1 times m-reduction [i] would yield (16, 30, 5190)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 42426 701433 193619 424838 964625 > 9³⁰ [i]