MinT - Best Known (137−72, 137, s)-Nets in Base 8

Best Known (137−72, 137, s)-Nets in Base 8

(137−72, 137, 130)-Net over F₈ — Constructive and digital

Digital (65, 137, 130)-net over F₈, using

2 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)

(137−72, 137, 185)-Net over F₈ — Digital

Digital (65, 137, 185)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−72, 137, 5554)-Net in Base 8 — Upper bound on s

There is no (65, 137, 5555)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5310 567150 598133 196011 843163 126875 887727 668017 859668 462732 443617 867585 047196 481488 526027 319887 953023 900664 905589 054855 439868 > 8¹³⁷ [i]