MinT - Best Known (67−33, 67, s)-Nets in Base 9

Best Known (67−33, 67, s)-Nets in Base 9

(67−33, 67, 164)-Net over F₉ — Constructive and digital

Digital (34, 67, 164)-net over F₉, using

1 times m-reduction [i] based on digital (34, 68, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 34, 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]

(67−33, 67, 7330)-Net in Base 9 — Upper bound on s

There is no (34, 67, 7331)-net in base 9, because

1 times m-reduction [i] would yield (34, 66, 7331)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 955 931871 267856 396515 335033 670570 624206 448479 924253 393798 997377 > 9⁶⁶ [i]