MinT - Best Known (19, 19+20, s)-Nets in Base 9

Best Known (19, 19+20, s)-Nets in Base 9

(19, 19+20, 82)-Net over F₉ — Constructive and digital

Digital (19, 39, 82)-net over F₉, using

base reduction for projective spaces (embedding PG(19,81) in PG(38,9)) for nets [i] based on digital (0, 20, 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]

(19, 19+20, 90)-Net over F₉ — Digital

Digital (19, 39, 90)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(19, 19+20, 2975)-Net in Base 9 — Upper bound on s

There is no (19, 39, 2976)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 16 437812 172738 013254 010601 960500 528641 > 9³⁹ [i]