MinT - Best Known (82, 82+67, s)-Nets in Base 8

Best Known (82, 82+67, s)-Nets in Base 8

(82, 82+67, 354)-Net over F₈ — Constructive and digital

Digital (82, 149, 354)-net over F₈, using

1 times m-reduction [i] based on digital (82, 150, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 75, 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]

(82, 82+67, 377)-Net over F₈ — Digital

Digital (82, 149, 377)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+67, 21088)-Net in Base 8 — Upper bound on s

There is no (82, 149, 21089)-net in base 8, because

1 times m-reduction [i] would yield (82, 148, 21089)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 442595 582664 656432 717834 908284 405843 141747 925551 946101 324202 868166 322277 742453 299229 299039 456629 591172 454046 822018 382563 630444 324920 > 8¹⁴⁸ [i]