MinT - Best Known (163−73, 163, s)-Nets in Base 8

Best Known (163−73, 163, s)-Nets in Base 8

(163−73, 163, 354)-Net over F₈ — Constructive and digital

Digital (90, 163, 354)-net over F₈, using

3 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]

(163−73, 163, 415)-Net over F₈ — Digital

Digital (90, 163, 415)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−73, 163, 23611)-Net in Base 8 — Upper bound on s

There is no (90, 163, 23612)-net in base 8, because

1 times m-reduction [i] would yield (90, 162, 23612)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 199 873625 654236 573084 869591 589014 437068 679912 088307 578024 961304 207666 125683 847290 252377 068651 650454 478767 377513 457185 859934 820423 487536 538442 539530 > 8¹⁶² [i]