MinT - Best Known (87, 87+61, s)-Nets in Base 8

Best Known (87, 87+61, s)-Nets in Base 8

(87, 87+61, 354)-Net over F₈ — Constructive and digital

Digital (87, 148, 354)-net over F₈, using

12 times m-reduction [i] based on digital (87, 160, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 80, 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, 87+61, 550)-Net over F₈ — Digital

Digital (87, 148, 550)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+61, 45777)-Net in Base 8 — Upper bound on s

There is no (87, 148, 45778)-net in base 8, because

1 times m-reduction [i] would yield (87, 147, 45778)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 679765 224046 795257 223929 944877 726304 515818 764110 337888 590697 583679 673924 747693 847258 233153 416092 882156 719405 938304 365002 717885 513440 > 8¹⁴⁷ [i]