MinT - Best Known (111−49, 111, s)-Nets in Base 8

Best Known (111−49, 111, s)-Nets in Base 8

(111−49, 111, 256)-Net over F₈ — Constructive and digital

Digital (62, 111, 256)-net over F₈, using

3 times m-reduction [i] based on digital (62, 114, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 57, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(111−49, 111, 322)-Net over F₈ — Digital

Digital (62, 111, 322)-net over F₈, using

1 times m-reduction [i] based on digital (62, 112, 322)-net over F₈, using
- trace code for nets [i] based on digital (6, 56, 161)-net over F₆₄, using
  - net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(111−49, 111, 19279)-Net in Base 8 — Upper bound on s

There is no (62, 111, 19280)-net in base 8, because

1 times m-reduction [i] would yield (62, 110, 19280)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2189 180458 466982 518189 004359 908708 380087 541945 700148 700068 094442 747723 281358 670499 625171 703498 353356 > 8¹¹⁰ [i]