MinT - Best Known (88, 88+61, s)-Nets in Base 8

Best Known (88, 88+61, s)-Nets in Base 8

(88, 88+61, 354)-Net over F₈ — Constructive and digital

Digital (88, 149, 354)-net over F₈, using

13 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+61, 570)-Net over F₈ — Digital

Digital (88, 149, 570)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+61, 49064)-Net in Base 8 — Upper bound on s

There is no (88, 149, 49065)-net in base 8, because

1 times m-reduction [i] would yield (88, 148, 49065)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 438300 776419 446698 187290 973716 889133 872237 651741 215903 045640 725778 751513 059979 268715 065342 801501 557896 886302 443471 119166 759725 865904 > 8¹⁴⁸ [i]