MinT - Best Known (60, 60+47, s)-Nets in Base 8

Best Known (60, 60+47, s)-Nets in Base 8

(60, 60+47, 256)-Net over F₈ — Constructive and digital

Digital (60, 107, 256)-net over F₈, using

3 times m-reduction [i] based on digital (60, 110, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 55, 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]

(60, 60+47, 322)-Net over F₈ — Digital

Digital (60, 107, 322)-net over F₈, using

1 times m-reduction [i] based on digital (60, 108, 322)-net over F₈, using
- trace code for nets [i] based on digital (6, 54, 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]

(60, 60+47, 19548)-Net in Base 8 — Upper bound on s

There is no (60, 107, 19549)-net in base 8, because

1 times m-reduction [i] would yield (60, 106, 19549)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534466 127855 629080 740211 036537 535120 469508 917922 441097 653965 839679 296437 118403 687744 617411 471640 > 8¹⁰⁶ [i]