MinT - Best Known (74, 74+51, s)-Nets in Base 3

Best Known (74, 74+51, s)-Nets in Base 3

(74, 74+51, 80)-Net over F₃ — Constructive and digital

Digital (74, 125, 80)-net over F₃, using

7 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, 74+51, 119)-Net over F₃ — Digital

Digital (74, 125, 119)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+51, 1159)-Net in Base 3 — Upper bound on s

There is no (74, 125, 1160)-net in base 3, because

1 times m-reduction [i] would yield (74, 124, 1160)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 148443 123734 051684 197673 178471 193652 477516 164341 436947 907985 > 3¹²⁴ [i]