MinT - Best Known (57, 80, s)-Nets in Base 3

Best Known (57, 80, s)-Nets in Base 3

(57, 80, 156)-Net over F₃ — Constructive and digital

Digital (57, 80, 156)-net over F₃, using

1 times m-reduction [i] based on digital (57, 81, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 27, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(57, 80, 254)-Net over F₃ — Digital

Digital (57, 80, 254)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 80, 6544)-Net in Base 3 — Upper bound on s

There is no (57, 80, 6545)-net in base 3, because

1 times m-reduction [i] would yield (57, 79, 6545)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 49 298435 391870 261198 585985 397301 520827 > 3⁷⁹ [i]