MinT - Best Known (58, 106, s)-Nets in Base 9

Best Known (58, 106, s)-Nets in Base 9

(58, 106, 320)-Net over F₉ — Constructive and digital

Digital (58, 106, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 53, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(58, 106, 334)-Net over F₉ — Digital

Digital (58, 106, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 53, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(58, 106, 20069)-Net in Base 9 — Upper bound on s

There is no (58, 106, 20070)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 141291 808700 885227 601631 480055 060989 592836 542929 504507 652580 086254 990295 994740 219377 761587 625098 077569 > 9¹⁰⁶ [i]