MinT - Best Known (60−32, 60, s)-Nets in Base 9

Best Known (60−32, 60, s)-Nets in Base 9

(60−32, 60, 78)-Net over F₉ — Constructive and digital

Digital (28, 60, 78)-net over F₉, using

t-expansion [i] based on digital (22, 60, 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]

(60−32, 60, 84)-Net in Base 9 — Constructive

(28, 60, 84)-net in base 9, using

base change [i] based on digital (8, 40, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(60−32, 60, 110)-Net over F₉ — Digital

Digital (28, 60, 110)-net over F₉, using

t-expansion [i] based on digital (26, 60, 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]

(60−32, 60, 3210)-Net in Base 9 — Upper bound on s

There is no (28, 60, 3211)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1801 252721 701478 128449 378372 429884 582631 073391 071234 457985 > 9⁶⁰ [i]