MinT - Best Known (53, 53+35, s)-Nets in Base 8

Best Known (53, 53+35, s)-Nets in Base 8

(53, 53+35, 354)-Net over F₈ — Constructive and digital

Digital (53, 88, 354)-net over F₈, using

4 times m-reduction [i] based on digital (53, 92, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 46, 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]

(53, 53+35, 435)-Net over F₈ — Digital

Digital (53, 88, 435)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+35, 42898)-Net in Base 8 — Upper bound on s

There is no (53, 88, 42899)-net in base 8, because

1 times m-reduction [i] would yield (53, 87, 42899)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 706759 894691 766251 725366 491562 741151 718355 447362 247281 229287 143394 825555 726262 > 8⁸⁷ [i]