MinT - Best Known (10, 21, s)-Nets in Base 9

Best Known (10, 21, s)-Nets in Base 9

(10, 21, 82)-Net over F₉ — Constructive and digital

Digital (10, 21, 82)-net over F₉, using

base reduction for projective spaces (embedding PG(10,81) in PG(20,9)) for nets [i] based on digital (0, 11, 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]

(10, 21, 2133)-Net in Base 9 — Upper bound on s

There is no (10, 21, 2134)-net in base 9, because

1 times m-reduction [i] would yield (10, 20, 2134)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 12 159313 976723 707377 > 9²⁰ [i]