MinT - Best Known (66, 66+45, s)-Nets in Base 8

Best Known (66, 66+45, s)-Nets in Base 8

(66, 66+45, 354)-Net over F₈ — Constructive and digital

Digital (66, 111, 354)-net over F₈, using

7 times m-reduction [i] based on digital (66, 118, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 59, 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]

(66, 66+45, 470)-Net over F₈ — Digital

Digital (66, 111, 470)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+45, 42370)-Net in Base 8 — Upper bound on s

There is no (66, 111, 42371)-net in base 8, because

1 times m-reduction [i] would yield (66, 110, 42371)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2187 648772 769963 650460 427879 877375 705803 595170 890050 911858 201654 328864 551325 549350 656899 924452 233184 > 8¹¹⁰ [i]