MinT - Best Known (56, 56+41, s)-Nets in Base 8

Best Known (56, 56+41, s)-Nets in Base 8

(56, 56+41, 354)-Net over F₈ — Constructive and digital

Digital (56, 97, 354)-net over F₈, using

1 times m-reduction [i] based on digital (56, 98, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 49, 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]

(56, 56+41, 25634)-Net in Base 8 — Upper bound on s

There is no (56, 97, 25635)-net in base 8, because

1 times m-reduction [i] would yield (56, 96, 25635)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 497 379571 004565 874179 028187 621183 562787 266551 032959 964878 518056 571028 297417 889501 673432 > 8⁹⁶ [i]