MinT - Best Known (171−51, 171, s)-Nets in Base 8

Best Known (171−51, 171, s)-Nets in Base 8

(171−51, 171, 1026)-Net over F₈ — Constructive and digital

Digital (120, 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]

(171−51, 171, 3438)-Net over F₈ — Digital

Digital (120, 171, 3438)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−51, 171, 2011575)-Net in Base 8 — Upper bound on s

There is no (120, 171, 2011576)-net in base 8, because

1 times m-reduction [i] would yield (120, 170, 2011576)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3351 972930 745913 861213 101822 117448 484902 933726 594427 701560 628123 320676 481104 976960 437319 433686 953350 096307 129100 507967 488120 609371 633601 071738 577644 242084 > 8¹⁷⁰ [i]