MinT - Best Known (56, 103, s)-Nets in Base 8

Best Known (56, 103, s)-Nets in Base 8

(56, 103, 208)-Net over F₈ — Constructive and digital

Digital (56, 103, 208)-net over F₈, using

3 times m-reduction [i] based on digital (56, 106, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 53, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(56, 103, 260)-Net over F₈ — Digital

Digital (56, 103, 260)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 103, 13611)-Net in Base 8 — Upper bound on s

There is no (56, 103, 13612)-net in base 8, because

1 times m-reduction [i] would yield (56, 102, 13612)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 448586 958616 261841 254354 403516 749656 038093 724018 711873 888467 207787 431942 877056 676309 812564 > 8¹⁰² [i]