MinT - Best Known (9−5, 9, s)-Nets in Base 9

Best Known (9−5, 9, s)-Nets in Base 9

(9−5, 9, 82)-Net over F₉ — Constructive and digital

Digital (4, 9, 82)-net over F₉, using

base reduction for projective spaces (embedding PG(4,81) in PG(8,9)) for nets [i] based on digital (0, 5, 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]

(9−5, 9, 1159)-Net in Base 9 — Upper bound on s

There is no (4, 9, 1160)-net in base 9, because

1 times m-reduction [i] would yield (4, 8, 1160)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 43 114881 > 9⁸ [i]