MinT - Best Known (156−45, 156, s)-Nets in Base 8

Best Known (156−45, 156, s)-Nets in Base 8

(156−45, 156, 1026)-Net over F₈ — Constructive and digital

Digital (111, 156, 1026)-net over F₈, using

10 times m-reduction [i] based on digital (111, 166, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 83, 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]

(156−45, 156, 3946)-Net over F₈ — Digital

Digital (111, 156, 3946)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−45, 156, 2981483)-Net in Base 8 — Upper bound on s

There is no (111, 156, 2981484)-net in base 8, because

1 times m-reduction [i] would yield (111, 155, 2981484)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 268348 162112 745209 795211 798024 341414 571882 005786 024458 329239 492463 433151 640998 228824 805800 676367 110865 462904 856729 537584 399196 250839 486924 > 8¹⁵⁵ [i]