MinT - Best Known (58, 58+45, s)-Nets in Base 8

Best Known (58, 58+45, s)-Nets in Base 8

(58, 58+45, 256)-Net over F₈ — Constructive and digital

Digital (58, 103, 256)-net over F₈, using

3 times m-reduction [i] based on digital (58, 106, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 53, 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]

(58, 58+45, 322)-Net over F₈ — Digital

Digital (58, 103, 322)-net over F₈, using

1 times m-reduction [i] based on digital (58, 104, 322)-net over F₈, using
- trace code for nets [i] based on digital (6, 52, 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]

(58, 58+45, 19884)-Net in Base 8 — Upper bound on s

There is no (58, 103, 19885)-net in base 8, because

1 times m-reduction [i] would yield (58, 102, 19885)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 468285 043998 943755 303857 293555 209592 221936 631679 324962 477735 698869 119677 706147 294657 198952 > 8¹⁰² [i]