MinT - Best Known (74−25, 74, s)-Nets in Base 9

Best Known (74−25, 74, s)-Nets in Base 9

(74−25, 74, 344)-Net over F₉ — Constructive and digital

Digital (49, 74, 344)-net over F₉, using

10 times m-reduction [i] based on digital (49, 84, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 42, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(74−25, 74, 1085)-Net over F₉ — Digital

Digital (49, 74, 1085)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−25, 74, 421929)-Net in Base 9 — Upper bound on s

There is no (49, 74, 421930)-net in base 9, because

1 times m-reduction [i] would yield (49, 73, 421930)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4567 874965 560256 393573 511021 032167 846643 104303 366838 791474 310115 504961 > 9⁷³ [i]