MinT - Best Known (59−29, 59, s)-Nets in Base 8

Best Known (59−29, 59, s)-Nets in Base 8

(59−29, 59, 130)-Net over F₈ — Constructive and digital

Digital (30, 59, 130)-net over F₈, using

1 times m-reduction [i] based on digital (30, 60, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 30, 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]

(59−29, 59, 4752)-Net in Base 8 — Upper bound on s

There is no (30, 59, 4753)-net in base 8, because

1 times m-reduction [i] would yield (30, 58, 4753)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23953 616403 164107 066870 354118 590852 206863 879785 809976 > 8⁵⁸ [i]