MinT - Best Known (77, 77+63, s)-Nets in Base 8

Best Known (77, 77+63, s)-Nets in Base 8

(77, 77+63, 354)-Net over F₈ — Constructive and digital

Digital (77, 140, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 70, 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]

(77, 77+63, 356)-Net over F₈ — Digital

Digital (77, 140, 356)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+63, 19854)-Net in Base 8 — Upper bound on s

There is no (77, 140, 19855)-net in base 8, because

1 times m-reduction [i] would yield (77, 139, 19855)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 338959 409039 991828 852719 479663 143610 856497 673740 940149 162187 924423 476302 569607 369579 661731 599939 497370 235557 173408 927313 670848 > 8¹³⁹ [i]