MinT - Best Known (34, 70, s)-Nets in Base 8

Best Known (34, 70, s)-Nets in Base 8

(34, 70, 82)-Net over F₈ — Constructive and digital

Digital (34, 70, 82)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (2, 20, 17)-net over F₈, using
  - net from sequence [i] based on digital (2, 16)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 17, using
      - a function field by SÃ©mirat [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]

(34, 70, 118)-Net over F₈ — Digital

Digital (34, 70, 118)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(34, 70, 3496)-Net in Base 8 — Upper bound on s

There is no (34, 70, 3497)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1646 762657 753711 848512 608726 721641 266610 691609 866058 187080 605576 > 8⁷⁰ [i]