MinT - Best Known (28−12, 28, s)-Nets in Base 9

Best Known (28−12, 28, s)-Nets in Base 9

(28−12, 28, 232)-Net over F₉ — Constructive and digital

Digital (16, 28, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 14, 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]

(28−12, 28, 236)-Net over F₉ — Digital

Digital (16, 28, 236)-net over F₉, using

trace code for nets [i] based on digital (2, 14, 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]

(28−12, 28, 10620)-Net in Base 9 — Upper bound on s

There is no (16, 28, 10621)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 523 596858 902988 687561 104049 > 9²⁸ [i]