MinT - Best Known (27, 27+63, s)-Nets in Base 9

Best Known (27, 27+63, s)-Nets in Base 9

(27, 27+63, 78)-Net over F₉ — Constructive and digital

Digital (27, 90, 78)-net over F₉, using

t-expansion [i] based on digital (22, 90, 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]

(27, 27+63, 110)-Net over F₉ — Digital

Digital (27, 90, 110)-net over F₉, using

t-expansion [i] based on digital (26, 90, 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]

(27, 27+63, 833)-Net in Base 9 — Upper bound on s

There is no (27, 90, 834)-net in base 9, because

1 times m-reduction [i] would yield (27, 89, 834)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 635361 188119 570922 912074 062192 205429 134329 828257 857542 391717 980843 993088 837661 152433 > 9⁸⁹ [i]