MinT - Best Known (77, 77+61, s)-Nets in Base 8

Best Known (77, 77+61, s)-Nets in Base 8

(77, 77+61, 354)-Net over F₈ — Constructive and digital

Digital (77, 138, 354)-net over F₈, using

2 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+61, 380)-Net over F₈ — Digital

Digital (77, 138, 380)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+61, 22879)-Net in Base 8 — Upper bound on s

There is no (77, 138, 22880)-net in base 8, because

1 times m-reduction [i] would yield (77, 137, 22880)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5292 392208 880378 059525 299802 662855 050816 865429 676286 530928 088760 355421 573256 538132 013653 694033 973029 492109 840089 130199 759659 > 8¹³⁷ [i]