MinT - Best Known (30, 30+84, s)-Nets in Base 9

Best Known (30, 30+84, s)-Nets in Base 9

(30, 30+84, 78)-Net over F₉ — Constructive and digital

Digital (30, 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]

(30, 30+84, 110)-Net over F₉ — Digital

Digital (30, 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]

(30, 30+84, 777)-Net in Base 9 — Upper bound on s

There is no (30, 114, 778)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 190937 179687 801602 168002 495994 748190 292205 077745 043793 007210 528334 898881 451931 147767 440769 511714 411092 229089 > 9¹¹⁴ [i]