MinT - Best Known (168−74, 168, s)-Nets in Base 8

Best Known (168−74, 168, s)-Nets in Base 8

(168−74, 168, 354)-Net over F₈ — Constructive and digital

Digital (94, 168, 354)-net over F₈, using

t-expansion [i] based on digital (93, 168, 354)-net over F₈, using
- 4 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(168−74, 168, 457)-Net over F₈ — Digital

Digital (94, 168, 457)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−74, 168, 26360)-Net in Base 8 — Upper bound on s

There is no (94, 168, 26361)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 440208 592154 430692 603259 906720 989379 497009 291240 012463 577038 936899 010152 737756 281114 479271 030194 129288 905516 103387 762713 668903 838431 738281 806237 722248 > 8¹⁶⁸ [i]