MinT - Best Known (145−71, 145, s)-Nets in Base 8

Best Known (145−71, 145, s)-Nets in Base 8

(145−71, 145, 160)-Net over F₈ — Constructive and digital

Digital (74, 145, 160)-net over F₈, using

1 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]

(145−71, 145, 258)-Net over F₈ — Digital

Digital (74, 145, 258)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−71, 145, 10299)-Net in Base 8 — Upper bound on s

There is no (74, 145, 10300)-net in base 8, because

1 times m-reduction [i] would yield (74, 144, 10300)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11115 078944 130130 336285 587896 995664 740124 589877 756484 444074 037951 050590 019535 993757 616214 285105 869591 303745 122525 177927 927285 181185 > 8¹⁴⁴ [i]