MinT - Best Known (45−19, 45, s)-Nets in Base 8

Best Known (45−19, 45, s)-Nets in Base 8

(45−19, 45, 208)-Net over F₈ — Constructive and digital

Digital (26, 45, 208)-net over F₈, using

1 times m-reduction [i] based on digital (26, 46, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 23, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(45−19, 45, 226)-Net over F₈ — Digital

Digital (26, 45, 226)-net over F₈, using

1 times m-reduction [i] based on digital (26, 46, 226)-net over F₈, using
- trace code for nets [i] based on digital (3, 23, 113)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
      - a curve from the manYPoints database [i]

(45−19, 45, 15403)-Net in Base 8 — Upper bound on s

There is no (26, 45, 15404)-net in base 8, because

1 times m-reduction [i] would yield (26, 44, 15404)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5447 054816 223492 595370 111867 478599 326869 > 8⁴⁴ [i]