MinT - Best Known (125−80, 125, s)-Nets in Base 9

Best Known (125−80, 125, s)-Nets in Base 9

(125−80, 125, 81)-Net over F₉ — Constructive and digital

Digital (45, 125, 81)-net over F₉, using

t-expansion [i] based on digital (32, 125, 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]

(125−80, 125, 147)-Net over F₉ — Digital

Digital (45, 125, 147)-net over F₉, using

t-expansion [i] based on digital (43, 125, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(125−80, 125, 1866)-Net in Base 9 — Upper bound on s

There is no (45, 125, 1867)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 192024 437319 238340 514210 051137 632093 547699 517124 367335 633133 431878 095853 273118 972959 539959 033074 378704 973810 176682 623937 > 9¹²⁵ [i]