MinT - Best Known (87, 87+66, s)-Nets in Base 8

Best Known (87, 87+66, s)-Nets in Base 8

(87, 87+66, 354)-Net over F₈ — Constructive and digital

Digital (87, 153, 354)-net over F₈, using

7 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+66, 461)-Net over F₈ — Digital

Digital (87, 153, 461)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 87+66, 28906)-Net in Base 8 — Upper bound on s

There is no (87, 153, 28907)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 489063 849775 043200 908781 190938 184816 754078 708529 401278 694722 239932 590024 786055 491198 635757 041282 598135 474024 610523 628473 222582 490443 777170 > 8¹⁵³ [i]