MinT - Best Known (91−63, 91, s)-Nets in Base 9

Best Known (91−63, 91, s)-Nets in Base 9

(91−63, 91, 78)-Net over F₉ — Constructive and digital

Digital (28, 91, 78)-net over F₉, using

t-expansion [i] based on digital (22, 91, 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]

(91−63, 91, 110)-Net over F₉ — Digital

Digital (28, 91, 110)-net over F₉, using

t-expansion [i] based on digital (26, 91, 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]

(91−63, 91, 896)-Net in Base 9 — Upper bound on s

There is no (28, 91, 897)-net in base 9, because

1 times m-reduction [i] would yield (28, 90, 897)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 78 706743 543048 879800 431744 991620 769027 467663 640915 741561 741854 128231 662896 519706 171193 > 9⁹⁰ [i]