MinT - Best Known (70, 150, s)-Nets in Base 8

Best Known (70, 150, s)-Nets in Base 8

(70, 150, 130)-Net over F₈ — Constructive and digital

Digital (70, 150, 130)-net over F₈, using

4 times m-reduction [i] based on digital (70, 154, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 56, 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, 98, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(70, 150, 189)-Net over F₈ — Digital

Digital (70, 150, 189)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 150, 5461)-Net in Base 8 — Upper bound on s

There is no (70, 150, 5462)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2925 779930 553728 278221 922716 183413 516484 468048 762321 067057 267858 998546 339621 996615 936861 817848 766264 157033 524723 599164 595422 766253 546764 > 8¹⁵⁰ [i]