MinT - Best Known (71−36, 71, s)-Nets in Base 8

Best Known (71−36, 71, s)-Nets in Base 8

(71−36, 71, 89)-Net over F₈ — Constructive and digital

Digital (35, 71, 89)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (3, 21, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]
2. digital (14, 50, 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]

(71−36, 71, 126)-Net over F₈ — Digital

Digital (35, 71, 126)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(71−36, 71, 3926)-Net in Base 8 — Upper bound on s

There is no (35, 71, 3927)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13198 025102 037284 965758 370990 693493 953653 576813 537093 175060 067927 > 8⁷¹ [i]