MinT - Best Known (86, 86+61, s)-Nets in Base 8

Best Known (86, 86+61, s)-Nets in Base 8

(86, 86+61, 354)-Net over F₈ — Constructive and digital

Digital (86, 147, 354)-net over F₈, using

11 times m-reduction [i] based on digital (86, 158, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 79, 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]

(86, 86+61, 530)-Net over F₈ — Digital

Digital (86, 147, 530)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+61, 42710)-Net in Base 8 — Upper bound on s

There is no (86, 147, 42711)-net in base 8, because

1 times m-reduction [i] would yield (86, 146, 42711)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 709907 554741 429939 524598 425894 954920 808046 246744 770796 066379 767543 502900 035527 336847 954269 696571 109812 483386 316728 081087 744369 656808 > 8¹⁴⁶ [i]