MinT - Best Known (72, 72+79, s)-Nets in Base 8

Best Known (72, 72+79, s)-Nets in Base 8

(72, 72+79, 130)-Net over F₈ — Constructive and digital

Digital (72, 151, 130)-net over F₈, using

9 times m-reduction [i] based on digital (72, 160, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 58, 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, 102, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(72, 72+79, 205)-Net over F₈ — Digital

Digital (72, 151, 205)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+79, 6518)-Net in Base 8 — Upper bound on s

There is no (72, 151, 6519)-net in base 8, because

1 times m-reduction [i] would yield (72, 150, 6519)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2923 780342 887861 301976 550759 790016 945697 877036 568061 167259 282067 243472 398040 356707 804170 448963 617674 892141 848908 027125 164390 635669 379368 > 8¹⁵⁰ [i]