MinT - Best Known (22, 22+18, s)-Nets in Base 8

Best Known (22, 22+18, s)-Nets in Base 8

(22, 22+18, 160)-Net over F₈ — Constructive and digital

Digital (22, 40, 160)-net over F₈, using

2 times m-reduction [i] based on digital (22, 42, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 21, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(22, 22+18, 194)-Net over F₈ — Digital

Digital (22, 40, 194)-net over F₈, using

trace code for nets [i] based on digital (2, 20, 97)-net over F₆₄, using
- net from sequence [i] based on digital (2, 96)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 2 and N(F) ≥ 97, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(22, 22+18, 6109)-Net in Base 8 — Upper bound on s

There is no (22, 40, 6110)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 330053 587128 788208 083642 460717 961915 > 8⁴⁰ [i]