MinT - Best Known (87−41, 87, s)-Nets in Base 9

Best Known (87−41, 87, s)-Nets in Base 9

(87−41, 87, 232)-Net over F₉ — Constructive and digital

Digital (46, 87, 232)-net over F₉, using

1 times m-reduction [i] based on digital (46, 88, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 44, 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]

(87−41, 87, 236)-Net over F₉ — Digital

Digital (46, 87, 236)-net over F₉, using

1 times m-reduction [i] based on digital (46, 88, 236)-net over F₉, using
- trace code for nets [i] based on digital (2, 44, 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]

(87−41, 87, 13154)-Net in Base 9 — Upper bound on s

There is no (46, 87, 13155)-net in base 9, because

1 times m-reduction [i] would yield (46, 86, 13155)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11625 447078 011091 273675 758432 553248 728414 868523 392360 638071 417320 367258 394186 584801 > 9⁸⁶ [i]