MinT - Best Known (53−23, 53, s)-Nets in Base 8

Best Known (53−23, 53, s)-Nets in Base 8

(53−23, 53, 208)-Net over F₈ — Constructive and digital

Digital (30, 53, 208)-net over F₈, using

1 times m-reduction [i] based on digital (30, 54, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 27, 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]

(53−23, 53, 226)-Net over F₈ — Digital

Digital (30, 53, 226)-net over F₈, using

1 times m-reduction [i] based on digital (30, 54, 226)-net over F₈, using
- trace code for nets [i] based on digital (3, 27, 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]

(53−23, 53, 13027)-Net in Base 8 — Upper bound on s

There is no (30, 53, 13028)-net in base 8, because

1 times m-reduction [i] would yield (30, 52, 13028)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 91408 513946 901923 799565 831284 619075 956293 353548 > 8⁵² [i]