MinT - Best Known (161−85, 161, s)-Nets in Base 8

Best Known (161−85, 161, s)-Nets in Base 8

(161−85, 161, 130)-Net over F₈ — Constructive and digital

Digital (76, 161, 130)-net over F₈, using

11 times m-reduction [i] based on digital (76, 172, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 62, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]
  2. digital (14, 110, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(161−85, 161, 209)-Net over F₈ — Digital

Digital (76, 161, 209)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−85, 161, 6475)-Net in Base 8 — Upper bound on s

There is no (76, 161, 6476)-net in base 8, because

1 times m-reduction [i] would yield (76, 160, 6476)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 131283 932215 269956 920879 414677 311897 775298 910921 874673 197401 123692 135863 222609 202671 506965 962721 753414 809914 784885 657570 206328 899064 783975 753698 > 8¹⁶⁰ [i]