MinT - Best Known (121−91, 121, s)-Nets in Base 9

Best Known (121−91, 121, s)-Nets in Base 9

(121−91, 121, 78)-Net over F₉ — Constructive and digital

Digital (30, 121, 78)-net over F₉, using

t-expansion [i] based on digital (22, 121, 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]

(121−91, 121, 110)-Net over F₉ — Digital

Digital (30, 121, 110)-net over F₉, using

t-expansion [i] based on digital (26, 121, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(121−91, 121, 744)-Net in Base 9 — Upper bound on s

There is no (30, 121, 745)-net in base 9, because

1 times m-reduction [i] would yield (30, 120, 745)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 255452 133397 861592 823345 906099 768006 673784 172982 075838 682491 471443 400828 109149 061666 459608 862732 831191 741330 967849 > 9¹²⁰ [i]