MinT - Best Known (166−53, 166, s)-Nets in Base 8

Best Known (166−53, 166, s)-Nets in Base 8

(166−53, 166, 1026)-Net over F₈ — Constructive and digital

Digital (113, 166, 1026)-net over F₈, using

4 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]

(166−53, 166, 2233)-Net over F₈ — Digital

Digital (113, 166, 2233)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−53, 166, 811585)-Net in Base 8 — Upper bound on s

There is no (113, 166, 811586)-net in base 8, because

1 times m-reduction [i] would yield (113, 165, 811586)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 102294 860991 301653 539178 535538 606530 702041 332825 912046 234839 489171 027343 198764 681633 565627 304775 569527 664002 982764 994844 415134 214219 403513 304898 218912 > 8¹⁶⁵ [i]