MinT - Best Known (31, 31+74, s)-Nets in Base 9

Best Known (31, 31+74, s)-Nets in Base 9

(31, 31+74, 78)-Net over F₉ — Constructive and digital

Digital (31, 105, 78)-net over F₉, using

t-expansion [i] based on digital (22, 105, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(31, 31+74, 120)-Net over F₉ — Digital

Digital (31, 105, 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]

(31, 31+74, 912)-Net in Base 9 — Upper bound on s

There is no (31, 105, 913)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15981 589335 858989 577571 289064 500510 243999 135967 338546 418348 553577 069626 033001 116612 297467 397614 741033 > 9¹⁰⁵ [i]