MinT - Best Known (167−49, 167, s)-Nets in Base 8

Best Known (167−49, 167, s)-Nets in Base 8

(167−49, 167, 1026)-Net over F₈ — Constructive and digital

Digital (118, 167, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 167, 1026)-net over F₈, using
- 5 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]

(167−49, 167, 3737)-Net over F₈ — Digital

Digital (118, 167, 3737)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−49, 167, 2469644)-Net in Base 8 — Upper bound on s

There is no (118, 167, 2469645)-net in base 8, because

1 times m-reduction [i] would yield (118, 166, 2469645)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818349 862604 473662 796561 929841 129144 963617 083863 631731 461924 159929 431957 117662 553923 860664 356388 675055 012266 798145 418245 583936 753100 827165 055520 020688 > 8¹⁶⁶ [i]