MinT - Best Known (20, 20+19, s)-Nets in Base 9

Best Known (20, 20+19, s)-Nets in Base 9

(20, 20+19, 164)-Net over F₉ — Constructive and digital

Digital (20, 39, 164)-net over F₉, using

1 times m-reduction [i] based on digital (20, 40, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 20, 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]

(20, 20+19, 5537)-Net in Base 9 — Upper bound on s

There is no (20, 39, 5538)-net in base 9, because

1 times m-reduction [i] would yield (20, 38, 5538)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 827417 722953 933851 024199 544665 456785 > 9³⁸ [i]