MinT - Best Known (4, 4+4, s)-Nets in Base 8

Best Known (4, 4+4, s)-Nets in Base 8

(4, 4+4, 130)-Net over F₈ — Constructive and digital

Digital (4, 8, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 4, 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]

(4, 4+4, 826)-Net in Base 8 — Upper bound on s

There is no (4, 8, 827)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 788101 > 8⁸ [i]