MinT - Best Known (75−37, 75, s)-Nets in Base 9

Best Known (75−37, 75, s)-Nets in Base 9

(75−37, 75, 164)-Net over F₉ — Constructive and digital

Digital (38, 75, 164)-net over F₉, using

1 times m-reduction [i] based on digital (38, 76, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 38, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(75−37, 75, 166)-Net over F₉ — Digital

Digital (38, 75, 166)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−37, 75, 7896)-Net in Base 9 — Upper bound on s

There is no (38, 75, 7897)-net in base 9, because

1 times m-reduction [i] would yield (38, 74, 7897)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41136 480358 689759 723372 530305 890862 906789 452643 776420 309813 447295 717713 > 9⁷⁴ [i]