MinT - Best Known (54, 54+92, s)-Nets in Base 9

Best Known (54, 54+92, s)-Nets in Base 9

(54, 54+92, 81)-Net over F₉ — Constructive and digital

Digital (54, 146, 81)-net over F₉, using

t-expansion [i] based on digital (32, 146, 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]

(54, 54+92, 182)-Net over F₉ — Digital

Digital (54, 146, 182)-net over F₉, using

t-expansion [i] based on digital (50, 146, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(54, 54+92, 2375)-Net in Base 9 — Upper bound on s

There is no (54, 146, 2376)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 175252 933356 875514 616397 878804 250161 245807 618274 438602 372508 496684 083921 702906 760107 359291 726140 359180 608200 913037 998121 544953 044708 414081 > 9¹⁴⁶ [i]