MinT - Best Known (27, 27+110, s)-Nets in Base 9

Best Known (27, 27+110, s)-Nets in Base 9

(27, 27+110, 78)-Net over F₉ — Constructive and digital

Digital (27, 137, 78)-net over F₉, using

t-expansion [i] based on digital (22, 137, 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+110, 110)-Net over F₉ — Digital

Digital (27, 137, 110)-net over F₉, using

t-expansion [i] based on digital (26, 137, 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+110, 601)-Net in Base 9 — Upper bound on s

There is no (27, 137, 602)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 53990 910173 533260 887473 019706 649976 470030 649304 752248 766510 923931 424125 998602 489558 663962 112454 714326 288492 474978 244844 711879 831409 > 9¹³⁷ [i]