MinT - Best Known (45−19, 45, s)-Nets in Base 3

Best Known (45−19, 45, s)-Nets in Base 3

(45−19, 45, 56)-Net over F₃ — Constructive and digital

Digital (26, 45, 56)-net over F₃, using

1 times m-reduction [i] based on digital (26, 46, 56)-net over F₃, using
- trace code for nets [i] based on digital (3, 23, 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]

(45−19, 45, 437)-Net in Base 3 — Upper bound on s

There is no (26, 45, 438)-net in base 3, because

1 times m-reduction [i] would yield (26, 44, 438)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 993 826803 410595 684573 > 3⁴⁴ [i]