MinT - Best Known (150−65, 150, s)-Nets in Base 8

Best Known (150−65, 150, s)-Nets in Base 8

(150−65, 150, 354)-Net over F₈ — Constructive and digital

Digital (85, 150, 354)-net over F₈, using

6 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]

(150−65, 150, 450)-Net over F₈ — Digital

Digital (85, 150, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 75, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(150−65, 150, 29275)-Net in Base 8 — Upper bound on s

There is no (85, 150, 29276)-net in base 8, because

1 times m-reduction [i] would yield (85, 149, 29276)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 363 800992 321989 487430 069096 494574 555709 886482 071330 489379 733660 132148 340078 437968 744215 269342 878729 179554 503680 296764 066406 449617 392970 > 8¹⁴⁹ [i]