MinT - Best Known (65, 65+67, s)-Nets in Base 8

Best Known (65, 65+67, s)-Nets in Base 8

(65, 65+67, 130)-Net over F₈ — Constructive and digital

Digital (65, 132, 130)-net over F₈, using

7 times m-reduction [i] based on digital (65, 139, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 51, 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, 88, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(65, 65+67, 206)-Net over F₈ — Digital

Digital (65, 132, 206)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+67, 7211)-Net in Base 8 — Upper bound on s

There is no (65, 132, 7212)-net in base 8, because

1 times m-reduction [i] would yield (65, 131, 7212)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20251 483979 055890 574883 234759 767919 900445 110889 199446 538838 608078 240839 745510 558557 395938 132976 764477 528968 388057 745793 > 8¹³¹ [i]