MinT - Best Known (85, 156, s)-Nets in Base 8

Best Known (85, 156, s)-Nets in Base 8

(85, 156, 354)-Net over F₈ — Constructive and digital

Digital (85, 156, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 78, 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]

(85, 156, 374)-Net over F₈ — Digital

Digital (85, 156, 374)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 156, 19819)-Net in Base 8 — Upper bound on s

There is no (85, 156, 19820)-net in base 8, because

1 times m-reduction [i] would yield (85, 155, 19820)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 429713 650095 967576 510443 071740 989834 868214 590545 066389 828234 130305 396843 801572 660200 036873 736335 046816 725508 164590 453911 833225 760843 757049 > 8¹⁵⁵ [i]