MinT - Best Known (90, 90+65, s)-Nets in Base 8

Best Known (90, 90+65, s)-Nets in Base 8

(90, 90+65, 354)-Net over F₈ — Constructive and digital

Digital (90, 155, 354)-net over F₈, using

11 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 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]

(90, 90+65, 528)-Net over F₈ — Digital

Digital (90, 155, 528)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+65, 40521)-Net in Base 8 — Upper bound on s

There is no (90, 155, 40522)-net in base 8, because

1 times m-reduction [i] would yield (90, 154, 40522)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 911169 131334 593584 448753 636483 463096 541950 487612 551052 535287 664238 102582 665389 418882 166815 407837 690135 859403 164307 996059 462007 413412 474238 > 8¹⁵⁴ [i]