MinT - Best Known (17, 17+18, s)-Nets in Base 9

Best Known (17, 17+18, s)-Nets in Base 9

(17, 17+18, 82)-Net over F₉ — Constructive and digital

Digital (17, 35, 82)-net over F₉, using

base reduction for projective spaces (embedding PG(17,81) in PG(34,9)) for nets [i] based on digital (0, 18, 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]

(17, 17+18, 84)-Net over F₉ — Digital

Digital (17, 35, 84)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(17, 17+18, 2659)-Net in Base 9 — Upper bound on s

There is no (17, 35, 2660)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2508 998961 031326 377798 753492 678177 > 9³⁵ [i]