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

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

(42, 42+42, 130)-Net over F₈ — Constructive and digital

Digital (42, 84, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 42, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(42, 42+42, 153)-Net over F₈ — Digital

Digital (42, 84, 153)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

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

There is no (42, 84, 5066)-net in base 8, because

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]