MinT - Best Known (84−40, 84, s)-Nets in Base 8

Best Known (84−40, 84, s)-Nets in Base 8

(84−40, 84, 160)-Net over F₈ — Constructive and digital

Digital (44, 84, 160)-net over F₈, using

2 times m-reduction [i] based on digital (44, 86, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 43, 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]

(84−40, 84, 194)-Net over F₈ — Digital

Digital (44, 84, 194)-net over F₈, using

trace code for nets [i] based on digital (2, 42, 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]

(84−40, 84, 7352)-Net in Base 8 — Upper bound on s

There is no (44, 84, 7353)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7239 436591 943889 066556 663029 577462 610878 822675 331724 799438 067389 848674 065846 > 8⁸⁴ [i]