MinT - Best Known (82, 82+57, s)-Nets in Base 8

Best Known (82, 82+57, s)-Nets in Base 8

(82, 82+57, 354)-Net over F₈ — Constructive and digital

Digital (82, 139, 354)-net over F₈, using

11 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+57, 534)-Net over F₈ — Digital

Digital (82, 139, 534)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+57, 45570)-Net in Base 8 — Upper bound on s

There is no (82, 139, 45571)-net in base 8, because

1 times m-reduction [i] would yield (82, 138, 45571)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42320 639873 144785 800963 171292 744934 702149 450038 139736 967348 177680 178882 440712 389033 795971 368782 586647 567781 736231 398547 914624 > 8¹³⁸ [i]