MinT - Best Known (87, 87+73, s)-Nets in Base 8

Best Known (87, 87+73, s)-Nets in Base 8

(87, 87+73, 354)-Net over F₈ — Constructive and digital

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+73, 378)-Net over F₈ — Digital

Digital (87, 160, 378)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+73, 19851)-Net in Base 8 — Upper bound on s

There is no (87, 160, 19852)-net in base 8, because

1 times m-reduction [i] would yield (87, 159, 19852)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390628 641732 631313 879605 506495 248277 583603 648641 520771 674184 333623 105109 993015 832131 446934 916702 675167 194606 606202 118394 329297 499576 081520 706440 > 8¹⁵⁹ [i]