MinT - Best Known (56, 56+45, s)-Nets in Base 8

Best Known (56, 56+45, s)-Nets in Base 8

(56, 56+45, 256)-Net over F₈ — Constructive and digital

Digital (56, 101, 256)-net over F₈, using

1 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+45, 284)-Net over F₈ — Digital

Digital (56, 101, 284)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+45, 16456)-Net in Base 8 — Upper bound on s

There is no (56, 101, 16457)-net in base 8, because

1 times m-reduction [i] would yield (56, 100, 16457)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 037137 560933 364475 457843 121477 567863 218889 483490 097791 184817 570801 328670 969660 482933 733072 > 8¹⁰⁰ [i]