MinT - Best Known (56, 56+43, s)-Nets in Base 8

Best Known (56, 56+43, s)-Nets in Base 8

(56, 56+43, 256)-Net over F₈ — Constructive and digital

Digital (56, 99, 256)-net over F₈, using

3 times m-reduction [i] based on digital (56, 102, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 51, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(56, 56+43, 322)-Net over F₈ — Digital

Digital (56, 99, 322)-net over F₈, using

1 times m-reduction [i] based on digital (56, 100, 322)-net over F₈, using
- trace code for nets [i] based on digital (6, 50, 161)-net over F₆₄, using
  - net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(56, 56+43, 20301)-Net in Base 8 — Upper bound on s

There is no (56, 99, 20302)-net in base 8, because

1 times m-reduction [i] would yield (56, 98, 20302)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 31832 234543 499871 207450 467456 445356 906860 087686 652000 925124 410003 485701 358308 044653 236180 > 8⁹⁸ [i]