MinT - Best Known (50, 50+41, s)-Nets in Base 3

Best Known (50, 50+41, s)-Nets in Base 3

(50, 50+41, 60)-Net over F₃ — Constructive and digital

Digital (50, 91, 60)-net over F₃, using

1 times m-reduction [i] based on digital (50, 92, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 46, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]

(50, 50+41, 70)-Net over F₃ — Digital

Digital (50, 91, 70)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+41, 563)-Net in Base 3 — Upper bound on s

There is no (50, 91, 564)-net in base 3, because

1 times m-reduction [i] would yield (50, 90, 564)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 939285 504032 676594 589370 410500 944532 453569 > 3⁹⁰ [i]