MinT - Best Known (90−46, 90, s)-Nets in Base 8

Best Known (90−46, 90, s)-Nets in Base 8

(90−46, 90, 99)-Net over F₈ — Constructive and digital

Digital (44, 90, 99)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (7, 30, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (14, 60, 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]

(90−46, 90, 147)-Net over F₈ — Digital

Digital (44, 90, 147)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−46, 90, 4590)-Net in Base 8 — Upper bound on s

There is no (44, 90, 4591)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1903 846965 281142 499508 073181 385233 350364 049006 014862 545813 790288 691936 871438 439456 > 8⁹⁰ [i]