MinT - Best Known (171−79, 171, s)-Nets in Base 8

Best Known (171−79, 171, s)-Nets in Base 8

(171−79, 171, 256)-Net over F₈ — Constructive and digital

Digital (92, 171, 256)-net over F₈, using

t-expansion [i] based on digital (91, 171, 256)-net over F₈, using
- 1 times m-reduction [i] based on digital (91, 172, 256)-net over F₈, using
  - trace code for nets [i] based on digital (5, 86, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]

(171−79, 171, 380)-Net over F₈ — Digital

Digital (92, 171, 380)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−79, 171, 18980)-Net in Base 8 — Upper bound on s

There is no (92, 171, 18981)-net in base 8, because

1 times m-reduction [i] would yield (92, 170, 18981)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3354 178616 230148 848802 480790 487431 016327 434518 073377 454565 834376 840844 324791 519380 857549 393009 193054 641944 736033 930963 483794 525382 321229 871177 272358 736896 > 8¹⁷⁰ [i]