MinT - Best Known (33−13, 33, s)-Nets in Base 3

Best Known (33−13, 33, s)-Nets in Base 3

(33−13, 33, 56)-Net over F₃ — Constructive and digital

Digital (20, 33, 56)-net over F₃, using

1 times m-reduction [i] based on digital (20, 34, 56)-net over F₃, using
- trace code for nets [i] based on digital (3, 17, 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]

(33−13, 33, 519)-Net in Base 3 — Upper bound on s

There is no (20, 33, 520)-net in base 3, because

1 times m-reduction [i] would yield (20, 32, 520)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1871 390455 157809 > 3³² [i]