MinT - Best Known (27, 27+80, s)-Nets in Base 9

Best Known (27, 27+80, s)-Nets in Base 9

(27, 27+80, 78)-Net over F₉ — Constructive and digital

Digital (27, 107, 78)-net over F₉, using

t-expansion [i] based on digital (22, 107, 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+80, 110)-Net over F₉ — Digital

Digital (27, 107, 110)-net over F₉, using

t-expansion [i] based on digital (26, 107, 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+80, 679)-Net in Base 9 — Upper bound on s

There is no (27, 107, 680)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 321611 192794 906717 198818 114653 797866 575783 220775 469198 904048 959084 481048 450389 876286 619658 976867 249665 > 9¹⁰⁷ [i]