MinT - Best Known (40, 40+39, s)-Nets in Base 8

Best Known (40, 40+39, s)-Nets in Base 8

(40, 40+39, 130)-Net over F₈ — Constructive and digital

Digital (40, 79, 130)-net over F₈, using

1 times m-reduction [i] based on digital (40, 80, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 40, 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]

(40, 40+39, 153)-Net over F₈ — Digital

Digital (40, 79, 153)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+39, 5763)-Net in Base 8 — Upper bound on s

There is no (40, 79, 5764)-net in base 8, because

1 times m-reduction [i] would yield (40, 78, 5764)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 27686 359677 967763 186102 252884 593190 211864 143668 667519 365623 746160 450728 > 8⁷⁸ [i]