MinT - Best Known (159−43, 159, s)-Nets in Base 8

Best Known (159−43, 159, s)-Nets in Base 8

(159−43, 159, 1026)-Net over F₈ — Constructive and digital

Digital (116, 159, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 159, 1026)-net over F₈, using
- 13 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]

(159−43, 159, 6209)-Net over F₈ — Digital

Digital (116, 159, 6209)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−43, 159, 7728066)-Net in Base 8 — Upper bound on s

There is no (116, 159, 7728067)-net in base 8, because

1 times m-reduction [i] would yield (116, 158, 7728067)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48777 408351 420097 177073 443254 976860 868721 643455 943450 566906 532966 539984 366067 351990 142977 191811 255199 325764 062349 871829 000189 870643 955885 736800 > 8¹⁵⁸ [i]