MinT - Best Known (118−90, 118, s)-Nets in Base 9

Best Known (118−90, 118, s)-Nets in Base 9

(118−90, 118, 78)-Net over F₉ — Constructive and digital

Digital (28, 118, 78)-net over F₉, using

t-expansion [i] based on digital (22, 118, 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]

(118−90, 118, 110)-Net over F₉ — Digital

Digital (28, 118, 110)-net over F₉, using

t-expansion [i] based on digital (26, 118, 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]

(118−90, 118, 673)-Net in Base 9 — Upper bound on s

There is no (28, 118, 674)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 42385 827625 002094 278308 008453 215241 488385 471116 660948 866533 249171 458269 676812 291629 674191 406817 857805 336073 089617 > 9¹¹⁸ [i]