MinT - Best Known (107−76, 107, s)-Nets in Base 9

Best Known (107−76, 107, s)-Nets in Base 9

(107−76, 107, 78)-Net over F₉ — Constructive and digital

Digital (31, 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]

(107−76, 107, 120)-Net over F₉ — Digital

Digital (31, 107, 120)-net over F₉, using

net from sequence [i] based on digital (31, 119)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
  - a curve from the manYPoints database [i]

(107−76, 107, 890)-Net in Base 9 — Upper bound on s

There is no (31, 107, 891)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 306950 982891 070662 216460 051480 039399 677485 726525 311871 244682 299069 475808 881000 364395 571160 319687 397265 > 9¹⁰⁷ [i]