MinT - Best Known (162−73, 162, s)-Nets in Base 8

Best Known (162−73, 162, s)-Nets in Base 8

(162−73, 162, 354)-Net over F₈ — Constructive and digital

Digital (89, 162, 354)-net over F₈, using

2 times m-reduction [i] based on digital (89, 164, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 82, 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]

(162−73, 162, 402)-Net over F₈ — Digital

Digital (89, 162, 402)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−73, 162, 22285)-Net in Base 8 — Upper bound on s

There is no (89, 162, 22286)-net in base 8, because

1 times m-reduction [i] would yield (89, 161, 22286)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 004766 172899 801554 062107 204559 964346 402540 877726 931040 402537 547016 474586 829716 855199 190881 708889 362456 403704 203265 042261 342606 044295 326015 500280 > 8¹⁶¹ [i]