MinT - Best Known (86−54, 86, s)-Nets in Base 9

Best Known (86−54, 86, s)-Nets in Base 9

(86−54, 86, 81)-Net over F₉ — Constructive and digital

Digital (32, 86, 81)-net over F₉, using

net from sequence [i] based on digital (32, 80)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
  - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(86−54, 86, 120)-Net over F₉ — Digital

Digital (32, 86, 120)-net over F₉, using

t-expansion [i] based on digital (31, 86, 120)-net over F₉, using
- net from sequence [i] based on digital (31, 119)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
    - a curve from the manYPoints database [i]

(86−54, 86, 1479)-Net in Base 9 — Upper bound on s

There is no (32, 86, 1480)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11806 556918 702881 562733 143418 038391 193931 073139 964714 084353 844086 419579 888041 816001 > 9⁸⁶ [i]