MinT - Best Known (143−69, 143, s)-Nets in Base 8

Best Known (143−69, 143, s)-Nets in Base 8

(143−69, 143, 160)-Net over F₈ — Constructive and digital

Digital (74, 143, 160)-net over F₈, using

3 times m-reduction [i] based on digital (74, 146, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 73, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(143−69, 143, 271)-Net over F₈ — Digital

Digital (74, 143, 271)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−69, 143, 11410)-Net in Base 8 — Upper bound on s

There is no (74, 143, 11411)-net in base 8, because

1 times m-reduction [i] would yield (74, 142, 11411)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 687919 444718 236719 438349 550686 079653 392324 755304 422471 887197 189938 879349 265293 800093 391830 017906 575959 020044 574118 120190 799540 > 8¹⁴² [i]