MinT - Best Known (87−40, 87, s)-Nets in Base 3

Best Known (87−40, 87, s)-Nets in Base 3

(87−40, 87, 56)-Net over F₃ — Constructive and digital

Digital (47, 87, 56)-net over F₃, using

1 times m-reduction [i] based on digital (47, 88, 56)-net over F₃, using
- trace code for nets [i] based on digital (3, 44, 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]

(87−40, 87, 64)-Net over F₃ — Digital

Digital (47, 87, 64)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−40, 87, 474)-Net in Base 3 — Upper bound on s

There is no (47, 87, 475)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 325283 654973 463759 899651 547180 044892 120761 > 3⁸⁷ [i]