MinT - Best Known (171−55, 171, s)-Nets in Base 8

Best Known (171−55, 171, s)-Nets in Base 8

(171−55, 171, 1026)-Net over F₈ — Constructive and digital

Digital (116, 171, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 171, 1026)-net over F₈, using
- 1 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 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]

(171−55, 171, 2196)-Net over F₈ — Digital

Digital (116, 171, 2196)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−55, 171, 757567)-Net in Base 8 — Upper bound on s

There is no (116, 171, 757568)-net in base 8, because

1 times m-reduction [i] would yield (116, 170, 757568)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3352 038434 792197 808077 750202 629168 874445 426186 920540 077390 896935 507265 859300 577522 420653 515781 465133 890731 629228 983921 747297 496033 827373 852669 717091 307069 > 8¹⁷⁰ [i]