MinT - Best Known (74−32, 74, s)-Nets in Base 8

Best Known (74−32, 74, s)-Nets in Base 8

(74−32, 74, 256)-Net over F₈ — Constructive and digital

Digital (42, 74, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 37, 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]

(74−32, 74, 266)-Net over F₈ — Digital

Digital (42, 74, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 37, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(74−32, 74, 14586)-Net in Base 8 — Upper bound on s

There is no (42, 74, 14587)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 746270 968647 377629 348625 370360 773282 074484 998388 855282 053167 658765 > 8⁷⁴ [i]