MinT - Best Known (117−87, 117, s)-Nets in Base 9

Best Known (117−87, 117, s)-Nets in Base 9

(117−87, 117, 78)-Net over F₉ — Constructive and digital

Digital (30, 117, 78)-net over F₉, using

t-expansion [i] based on digital (22, 117, 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]

(117−87, 117, 110)-Net over F₉ — Digital

Digital (30, 117, 110)-net over F₉, using

t-expansion [i] based on digital (26, 117, 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]

(117−87, 117, 765)-Net in Base 9 — Upper bound on s

There is no (30, 117, 766)-net in base 9, because

1 times m-reduction [i] would yield (30, 116, 766)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 500 904229 696971 022377 830764 096914 336135 233869 343702 899052 614442 852172 224357 187736 869100 310448 419923 474801 166097 > 9¹¹⁶ [i]