MinT - Best Known (156−44, 156, s)-Nets in Base 8

Best Known (156−44, 156, s)-Nets in Base 8

(156−44, 156, 1026)-Net over F₈ — Constructive and digital

Digital (112, 156, 1026)-net over F₈, using

12 times m-reduction [i] based on digital (112, 168, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 84, 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]

(156−44, 156, 4579)-Net over F₈ — Digital

Digital (112, 156, 4579)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−44, 156, 3277043)-Net in Base 8 — Upper bound on s

There is no (112, 156, 3277044)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 149310 881100 075724 649526 294352 195027 635829 225709 948406 287143 076162 262083 330925 942875 969848 168743 326799 828978 618092 306082 923085 016732 818616 > 8¹⁵⁶ [i]