MinT - Best Known (171−53, 171, s)-Nets in Base 8

Best Known (171−53, 171, s)-Nets in Base 8

(171−53, 171, 1026)-Net over F₈ — Constructive and digital

Digital (118, 171, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 171, 1026)-net over F₈, using
- 1 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(171−53, 171, 2721)-Net over F₈ — Digital

Digital (118, 171, 2721)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−53, 171, 1210621)-Net in Base 8 — Upper bound on s

There is no (118, 171, 1210622)-net in base 8, because

1 times m-reduction [i] would yield (118, 170, 1210622)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3351 998790 621311 558491 604964 220168 840113 176391 244153 188746 847838 069666 144030 736943 691492 425230 371531 520764 032062 309716 750419 960182 038032 955418 486201 125930 > 8¹⁷⁰ [i]