MinT - Best Known (168−77, 168, s)-Nets in Base 8

Best Known (168−77, 168, s)-Nets in Base 8

(168−77, 168, 354)-Net over F₈ — Constructive and digital

Digital (91, 168, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 84, 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]

(168−77, 168, 387)-Net over F₈ — Digital

Digital (91, 168, 387)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−77, 168, 19953)-Net in Base 8 — Upper bound on s

There is no (91, 168, 19954)-net in base 8, because

1 times m-reduction [i] would yield (91, 167, 19954)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 548097 714113 620695 715103 966595 980809 523663 630415 846480 106891 096357 688525 799292 330990 641272 574983 069440 243851 183626 268123 219339 590924 987895 848722 326360 > 8¹⁶⁷ [i]