MinT - Best Known (55−27, 55, s)-Nets in Base 8

Best Known (55−27, 55, s)-Nets in Base 8

(55−27, 55, 130)-Net over F₈ — Constructive and digital

Digital (28, 55, 130)-net over F₈, using

1 times m-reduction [i] based on digital (28, 56, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 28, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(55−27, 55, 4558)-Net in Base 8 — Upper bound on s

There is no (28, 55, 4559)-net in base 8, because

1 times m-reduction [i] would yield (28, 54, 4559)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 848108 345442 101732 750142 340821 727836 539986 092490 > 8⁵⁴ [i]