MinT - Best Known (34−17, 34, s)-Nets in Base 9

Best Known (34−17, 34, s)-Nets in Base 9

(34−17, 34, 164)-Net over F₉ — Constructive and digital

Digital (17, 34, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 17, 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]

(34−17, 34, 4058)-Net in Base 9 — Upper bound on s

There is no (17, 34, 4059)-net in base 9, because

1 times m-reduction [i] would yield (17, 33, 4059)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 30 931437 579153 615075 090772 110529 > 9³³ [i]