MinT - Best Known (50, 50+43, s)-Nets in Base 3

Best Known (50, 50+43, s)-Nets in Base 3

(50, 50+43, 56)-Net over F₃ — Constructive and digital

Digital (50, 93, 56)-net over F₃, using

1 times m-reduction [i] based on digital (50, 94, 56)-net over F₃, using
- trace code for nets [i] based on digital (3, 47, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]

(50, 50+43, 66)-Net over F₃ — Digital

Digital (50, 93, 66)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+43, 514)-Net in Base 3 — Upper bound on s

There is no (50, 93, 515)-net in base 3, because

1 times m-reduction [i] would yield (50, 92, 515)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 81 611666 964949 236591 527727 737018 155237 185759 > 3⁹² [i]