MinT - Best Known (28, 28+92, s)-Nets in Base 9

Best Known (28, 28+92, s)-Nets in Base 9

(28, 28+92, 78)-Net over F₉ — Constructive and digital

Digital (28, 120, 78)-net over F₉, using

t-expansion [i] based on digital (22, 120, 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]

(28, 28+92, 110)-Net over F₉ — Digital

Digital (28, 120, 110)-net over F₉, using

t-expansion [i] based on digital (26, 120, 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]

(28, 28+92, 666)-Net in Base 9 — Upper bound on s

There is no (28, 120, 667)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 392692 041041 641299 997324 553055 355169 158664 674994 162191 609296 723246 370084 009386 306778 339833 632089 362738 206334 205521 > 9¹²⁰ [i]