MinT - Best Known (57, 57+35, s)-Nets in Base 3

Best Known (57, 57+35, s)-Nets in Base 3

(57, 57+35, 80)-Net over F₃ — Constructive and digital

Digital (57, 92, 80)-net over F₃, using

6 times m-reduction [i] based on digital (57, 98, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 49, 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]

(57, 57+35, 114)-Net over F₃ — Digital

Digital (57, 92, 114)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+35, 1268)-Net in Base 3 — Upper bound on s

There is no (57, 92, 1269)-net in base 3, because

1 times m-reduction [i] would yield (57, 91, 1269)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 312427 467370 662602 385954 593729 422107 693995 > 3⁹¹ [i]