MinT - Best Known (18, 18+17, s)-Nets in Base 9

Best Known (18, 18+17, s)-Nets in Base 9

(18, 18+17, 164)-Net over F₉ — Constructive and digital

Digital (18, 35, 164)-net over F₉, using

1 times m-reduction [i] based on digital (18, 36, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 18, 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]

(18, 18+17, 5342)-Net in Base 9 — Upper bound on s

There is no (18, 35, 5343)-net in base 9, because

1 times m-reduction [i] would yield (18, 34, 5343)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 278 230618 599807 232595 300781 139905 > 9³⁴ [i]