MinT - Best Known (85, 85+69, s)-Nets in Base 8

Best Known (85, 85+69, s)-Nets in Base 8

(85, 85+69, 354)-Net over F₈ — Constructive and digital

Digital (85, 154, 354)-net over F₈, using

2 times m-reduction [i] based on digital (85, 156, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 78, 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]

(85, 85+69, 394)-Net over F₈ — Digital

Digital (85, 154, 394)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+69, 22380)-Net in Base 8 — Upper bound on s

There is no (85, 154, 22381)-net in base 8, because

1 times m-reduction [i] would yield (85, 153, 22381)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 489879 039957 385964 594800 384353 897139 935711 397262 192906 108147 826070 797491 293670 378274 874731 434782 220395 648946 044605 010980 262266 714525 939750 > 8¹⁵³ [i]