MinT - Best Known (74, 123, s)-Nets in Base 3

Best Known (74, 123, s)-Nets in Base 3

(74, 123, 80)-Net over F₃ — Constructive and digital

Digital (74, 123, 80)-net over F₃, using

9 times m-reduction [i] based on digital (74, 132, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 66, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(74, 123, 126)-Net over F₃ — Digital

Digital (74, 123, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 123, 1281)-Net in Base 3 — Upper bound on s

There is no (74, 123, 1282)-net in base 3, because

1 times m-reduction [i] would yield (74, 122, 1282)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16190 508876 890479 200134 952212 596521 594422 192255 021938 677489 > 3¹²² [i]