MinT - Best Known (77, 77+55, s)-Nets in Base 8

Best Known (77, 77+55, s)-Nets in Base 8

(77, 77+55, 354)-Net over F₈ — Constructive and digital

Digital (77, 132, 354)-net over F₈, using

8 times m-reduction [i] based on 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+55, 475)-Net over F₈ — Digital

Digital (77, 132, 475)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+55, 37564)-Net in Base 8 — Upper bound on s

There is no (77, 132, 37565)-net in base 8, because

1 times m-reduction [i] would yield (77, 131, 37565)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20187 194659 684922 096816 950210 343110 697645 118827 535506 714672 667911 542935 556383 444899 646627 604899 349748 842154 898837 317692 > 8¹³¹ [i]