MinT - Best Known (146−43, 146, s)-Nets in Base 8

Best Known (146−43, 146, s)-Nets in Base 8

(146−43, 146, 1026)-Net over F₈ — Constructive and digital

Digital (103, 146, 1026)-net over F₈, using

4 times m-reduction [i] based on digital (103, 150, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 75, 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]

(146−43, 146, 3272)-Net over F₈ — Digital

Digital (103, 146, 3272)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−43, 146, 2133109)-Net in Base 8 — Upper bound on s

There is no (103, 146, 2133110)-net in base 8, because

1 times m-reduction [i] would yield (103, 145, 2133110)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 88725 569505 477105 065556 764912 711584 398495 529065 628648 492529 506939 467628 013044 742732 380631 862638 139618 172058 916574 304445 263497 988477 > 8¹⁴⁵ [i]