MinT - Best Known (157−71, 157, s)-Nets in Base 8

Best Known (157−71, 157, s)-Nets in Base 8

(157−71, 157, 354)-Net over F₈ — Constructive and digital

Digital (86, 157, 354)-net over F₈, using

1 times m-reduction [i] based on digital (86, 158, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 79, 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]

(157−71, 157, 386)-Net over F₈ — Digital

Digital (86, 157, 386)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−71, 157, 21033)-Net in Base 8 — Upper bound on s

There is no (86, 157, 21034)-net in base 8, because

1 times m-reduction [i] would yield (86, 156, 21034)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 692003 516568 708494 756026 497407 934948 635163 507404 602757 056831 285537 134617 278753 876202 903294 243281 257226 766986 777473 765421 099458 497129 476540 > 8¹⁵⁶ [i]