MinT - Best Known (136−57, 136, s)-Nets in Base 8

Best Known (136−57, 136, s)-Nets in Base 8

(136−57, 136, 354)-Net over F₈ — Constructive and digital

Digital (79, 136, 354)-net over F₈, using

8 times m-reduction [i] based on digital (79, 144, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 72, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(136−57, 136, 474)-Net over F₈ — Digital

Digital (79, 136, 474)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−57, 136, 36465)-Net in Base 8 — Upper bound on s

There is no (79, 136, 36466)-net in base 8, because

1 times m-reduction [i] would yield (79, 135, 36466)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 82 661884 320835 983840 668099 154815 130100 787789 905026 900193 912418 454177 944615 181135 782622 984093 106441 388189 207290 559039 029048 > 8¹³⁵ [i]