MinT - Best Known (20, 20+21, s)-Nets in Base 9

Best Known (20, 20+21, s)-Nets in Base 9

(20, 20+21, 82)-Net over F₉ — Constructive and digital

Digital (20, 41, 82)-net over F₉, using

base reduction for projective spaces (embedding PG(20,81) in PG(40,9)) for nets [i] based on digital (0, 21, 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]

(20, 20+21, 93)-Net over F₉ — Digital

Digital (20, 41, 93)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(20, 20+21, 3708)-Net in Base 9 — Upper bound on s

There is no (20, 41, 3709)-net in base 9, because

1 times m-reduction [i] would yield (20, 40, 3709)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 148 057176 420973 031357 472997 913771 370705 > 9⁴⁰ [i]