MinT - Best Known (81−37, 81, s)-Nets in Base 8

Best Known (81−37, 81, s)-Nets in Base 8

(81−37, 81, 208)-Net over F₈ — Constructive and digital

Digital (44, 81, 208)-net over F₈, using

1 times m-reduction [i] based on digital (44, 82, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 41, 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]

(81−37, 81, 226)-Net over F₈ — Digital

Digital (44, 81, 226)-net over F₈, using

1 times m-reduction [i] based on digital (44, 82, 226)-net over F₈, using
- trace code for nets [i] based on digital (3, 41, 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]

(81−37, 81, 11125)-Net in Base 8 — Upper bound on s

There is no (44, 81, 11126)-net in base 8, because

1 times m-reduction [i] would yield (44, 80, 11126)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 767255 611735 439714 779330 020931 101167 978266 318289 579208 982378 161846 988134 > 8⁸⁰ [i]