MinT - Best Known (168−54, 168, s)-Nets in Base 8

Best Known (168−54, 168, s)-Nets in Base 8

(168−54, 168, 1026)-Net over F₈ — Constructive and digital

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]

(168−54, 168, 2171)-Net over F₈ — Digital

Digital (114, 168, 2171)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−54, 168, 649417)-Net in Base 8 — Upper bound on s

There is no (114, 168, 649418)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 375158 123766 925873 248269 517928 240652 599143 481423 241994 909583 045881 002387 955011 400460 767099 601671 936089 481820 677604 265517 750333 142010 045085 523621 580000 > 8¹⁶⁸ [i]