MinT - Best Known (67−30, 67, s)-Nets in Base 8

Best Known (67−30, 67, s)-Nets in Base 8

(67−30, 67, 208)-Net over F₈ — Constructive and digital

Digital (37, 67, 208)-net over F₈, using

1 times m-reduction [i] based on digital (37, 68, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 34, 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]

(67−30, 67, 226)-Net over F₈ — Digital

Digital (37, 67, 226)-net over F₈, using

1 times m-reduction [i] based on digital (37, 68, 226)-net over F₈, using
- trace code for nets [i] based on digital (3, 34, 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]

(67−30, 67, 9909)-Net in Base 8 — Upper bound on s

There is no (37, 67, 9910)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 214263 029394 644525 381234 608448 348521 651443 817254 696149 723576 > 8⁶⁷ [i]