MinT - Best Known (88, 88+63, s)-Nets in Base 8

Best Known (88, 88+63, s)-Nets in Base 8

(88, 88+63, 354)-Net over F₈ — Constructive and digital

Digital (88, 151, 354)-net over F₈, using

11 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 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]

(88, 88+63, 529)-Net over F₈ — Digital

Digital (88, 151, 529)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+63, 41545)-Net in Base 8 — Upper bound on s

There is no (88, 151, 41546)-net in base 8, because

1 times m-reduction [i] would yield (88, 150, 41546)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2908 819107 987525 436339 246026 145121 853739 666513 299297 760940 842097 294918 707918 323827 599224 917686 088168 181435 714249 503234 421934 885366 956960 > 8¹⁵⁰ [i]