MinT - Best Known (114−85, 114, s)-Nets in Base 9

Best Known (114−85, 114, s)-Nets in Base 9

(114−85, 114, 78)-Net over F₉ — Constructive and digital

Digital (29, 114, 78)-net over F₉, using

t-expansion [i] based on digital (22, 114, 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]

(114−85, 114, 110)-Net over F₉ — Digital

Digital (29, 114, 110)-net over F₉, using

t-expansion [i] based on digital (26, 114, 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]

(114−85, 114, 736)-Net in Base 9 — Upper bound on s

There is no (29, 114, 737)-net in base 9, because

1 times m-reduction [i] would yield (29, 113, 737)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685697 787068 255918 020830 289061 136552 455588 987520 167159 978161 263903 218826 874185 149446 461681 737253 069060 354705 > 9¹¹³ [i]