MinT - Best Known (42, 85, s)-Nets in Base 8

Best Known (42, 85, s)-Nets in Base 8

(42, 85, 99)-Net over F₈ — Constructive and digital

Digital (42, 85, 99)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (7, 28, 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, 57, 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]

(42, 85, 146)-Net over F₈ — Digital

Digital (42, 85, 146)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 85, 5065)-Net in Base 8 — Upper bound on s

There is no (42, 85, 5066)-net in base 8, because

1 times m-reduction [i] would yield (42, 84, 5066)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7245 007078 406453 932575 389057 103550 315423 152188 157960 972423 754813 967103 300104 > 8⁸⁴ [i]