MinT - Best Known (37, 37+36, s)-Nets in Base 8

Best Known (37, 37+36, s)-Nets in Base 8

(37, 37+36, 130)-Net over F₈ — Constructive and digital

Digital (37, 73, 130)-net over F₈, using

1 times m-reduction [i] based on digital (37, 74, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 37, 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]

(37, 37+36, 144)-Net over F₈ — Digital

Digital (37, 73, 144)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(37, 37+36, 4949)-Net in Base 8 — Upper bound on s

There is no (37, 73, 4950)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 842888 525703 914285 313011 395098 877808 028079 592747 376787 231554 173146 > 8⁷³ [i]