MinT - Best Known (38, 72, s)-Nets in Base 9

Best Known (38, 72, s)-Nets in Base 9

(38, 72, 232)-Net over F₉ — Constructive and digital

Digital (38, 72, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 36, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(38, 72, 236)-Net over F₉ — Digital

Digital (38, 72, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 36, 118)-net over F₈₁, using
- net from sequence [i] based on digital (2, 117)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 118, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(38, 72, 9860)-Net in Base 9 — Upper bound on s

There is no (38, 72, 9861)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 507 799164 238982 950039 515076 741093 361016 207453 492149 781774 450242 118825 > 9⁷² [i]