MinT - Best Known (65−30, 65, s)-Nets in Base 9

Best Known (65−30, 65, s)-Nets in Base 9

(65−30, 65, 232)-Net over F₉ — Constructive and digital

Digital (35, 65, 232)-net over F₉, using

1 times m-reduction [i] based on digital (35, 66, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 33, 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]

(65−30, 65, 236)-Net over F₉ — Digital

Digital (35, 65, 236)-net over F₉, using

1 times m-reduction [i] based on digital (35, 66, 236)-net over F₉, using
- trace code for nets [i] based on digital (2, 33, 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]

(65−30, 65, 10949)-Net in Base 9 — Upper bound on s

There is no (35, 65, 10950)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 106 252335 783530 682269 412645 744613 460608 400002 055802 400813 702161 > 9⁶⁵ [i]