MinT - Best Known (168−46, 168, s)-Nets in Base 8

Best Known (168−46, 168, s)-Nets in Base 8

(168−46, 168, 1026)-Net over F₈ — Constructive and digital

Digital (122, 168, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 168, 1026)-net over F₈, using
- 4 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(168−46, 168, 5946)-Net over F₈ — Digital

Digital (122, 168, 5946)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−46, 168, 5319128)-Net in Base 8 — Upper bound on s

There is no (122, 168, 5319129)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 374434 625476 704013 294405 781458 732379 645213 835689 489254 492704 720638 163440 314272 704044 247346 325267 159045 399614 731709 771074 940109 769017 425379 124924 994280 > 8¹⁶⁸ [i]