MinT - Best Known (131−57, 131, s)-Nets in Base 8

Best Known (131−57, 131, s)-Nets in Base 8

(131−57, 131, 354)-Net over F₈ — Constructive and digital

Digital (74, 131, 354)-net over F₈, using

3 times m-reduction [i] based on digital (74, 134, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 67, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(131−57, 131, 389)-Net over F₈ — Digital

Digital (74, 131, 389)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−57, 131, 25149)-Net in Base 8 — Upper bound on s

There is no (74, 131, 25150)-net in base 8, because

1 times m-reduction [i] would yield (74, 130, 25150)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2524 205167 036450 823655 742307 292445 765918 794302 711618 085703 401288 893348 354061 503280 259954 607783 199871 857875 312577 611943 > 8¹³⁰ [i]