MinT - Best Known (89−63, 89, s)-Nets in Base 9

Best Known (89−63, 89, s)-Nets in Base 9

(89−63, 89, 78)-Net over F₉ — Constructive and digital

Digital (26, 89, 78)-net over F₉, using

t-expansion [i] based on digital (22, 89, 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]

(89−63, 89, 110)-Net over F₉ — Digital

Digital (26, 89, 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]

(89−63, 89, 775)-Net in Base 9 — Upper bound on s

There is no (26, 89, 776)-net in base 9, because

1 times m-reduction [i] would yield (26, 88, 776)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 972313 497715 803825 448867 824803 410757 643656 632787 724628 719197 982034 726628 363977 447617 > 9⁸⁸ [i]