MinT - Best Known (126−101, 126, s)-Nets in Base 9

Best Known (126−101, 126, s)-Nets in Base 9

(126−101, 126, 78)-Net over F₉ — Constructive and digital

Digital (25, 126, 78)-net over F₉, using

t-expansion [i] based on digital (22, 126, 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]

(126−101, 126, 96)-Net over F₉ — Digital

Digital (25, 126, 96)-net over F₉, using

net from sequence [i] based on digital (25, 95)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 25 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(126−101, 126, 561)-Net in Base 9 — Upper bound on s

There is no (25, 126, 562)-net in base 9, because

1 times m-reduction [i] would yield (25, 125, 562)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 198721 587021 066282 676906 776220 881017 343571 805631 829880 830916 552506 131360 199748 235439 607811 713001 154832 009710 611970 011873 > 9¹²⁵ [i]