MinT - Best Known (156−43, 156, s)-Nets in Base 8

Best Known (156−43, 156, s)-Nets in Base 8

(156−43, 156, 1026)-Net over F₈ — Constructive and digital

Digital (113, 156, 1026)-net over F₈, using

14 times m-reduction [i] based on digital (113, 170, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 85, 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]

(156−43, 156, 5355)-Net over F₈ — Digital

Digital (113, 156, 5355)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−43, 156, 5741927)-Net in Base 8 — Upper bound on s

There is no (113, 156, 5741928)-net in base 8, because

1 times m-reduction [i] would yield (113, 155, 5741928)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 268245 723636 563919 602728 408361 696617 232605 688616 561542 871356 891745 715626 689020 375580 253942 914692 548648 457021 346974 954502 803975 511291 180702 > 8¹⁵⁵ [i]