MinT - Best Known (61−27, 61, s)-Nets in Base 3

Best Known (61−27, 61, s)-Nets in Base 3

(61−27, 61, 56)-Net over F₃ — Constructive and digital

Digital (34, 61, 56)-net over F₃, using

1 times m-reduction [i] based on digital (34, 62, 56)-net over F₃, using
- trace code for nets [i] based on digital (3, 31, 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]

(61−27, 61, 438)-Net in Base 3 — Upper bound on s

There is no (34, 61, 439)-net in base 3, because

1 times m-reduction [i] would yield (34, 60, 439)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42449 367001 422044 662731 910935 > 3⁶⁰ [i]