MinT - Best Known (51, 51+35, s)-Nets in Base 8

Best Known (51, 51+35, s)-Nets in Base 8

(51, 51+35, 354)-Net over F₈ — Constructive and digital

Digital (51, 86, 354)-net over F₈, using

2 times m-reduction [i] based on digital (51, 88, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 44, 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]

(51, 51+35, 381)-Net over F₈ — Digital

Digital (51, 86, 381)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+35, 33586)-Net in Base 8 — Upper bound on s

There is no (51, 86, 33587)-net in base 8, because

1 times m-reduction [i] would yield (51, 85, 33587)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 57916 273378 331955 958833 437783 091984 603488 042601 445024 358803 273228 984959 931226 > 8⁸⁵ [i]