MinT - Best Known (87−35, 87, s)-Nets in Base 8

Best Known (87−35, 87, s)-Nets in Base 8

(87−35, 87, 354)-Net over F₈ — Constructive and digital

Digital (52, 87, 354)-net over F₈, using

3 times m-reduction [i] based on digital (52, 90, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 45, 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]

(87−35, 87, 407)-Net over F₈ — Digital

Digital (52, 87, 407)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−35, 87, 37957)-Net in Base 8 — Upper bound on s

There is no (52, 87, 37958)-net in base 8, because

1 times m-reduction [i] would yield (52, 86, 37958)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 463214 964845 466421 828383 069745 615191 783041 454687 616153 522891 487483 164163 171812 > 8⁸⁶ [i]