MinT - Best Known (20, 20+86, s)-Nets in Base 9

Best Known (20, 20+86, s)-Nets in Base 9

(20, 20+86, 74)-Net over F₉ — Constructive and digital

Digital (20, 106, 74)-net over F₉, using

t-expansion [i] based on digital (17, 106, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(20, 20+86, 84)-Net over F₉ — Digital

Digital (20, 106, 84)-net over F₉, using

t-expansion [i] based on digital (19, 106, 84)-net over F₉, using
- net from sequence [i] based on digital (19, 83)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
    - Drinfeld modules of rank 1 [i]

(20, 20+86, 449)-Net in Base 9 — Upper bound on s

There is no (20, 106, 450)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 153843 012927 383866 466687 581297 375170 608919 156673 177932 739828 730091 339899 462174 599483 821900 666640 560625 > 9¹⁰⁶ [i]