MinT - Best Known (56, 87, s)-Nets in Base 3

Best Known (56, 87, s)-Nets in Base 3

(56, 87, 80)-Net over F₃ — Constructive and digital

Digital (56, 87, 80)-net over F₃, using

9 times m-reduction [i] based on digital (56, 96, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 48, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(56, 87, 133)-Net over F₃ — Digital

Digital (56, 87, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 87, 1732)-Net in Base 3 — Upper bound on s

There is no (56, 87, 1733)-net in base 3, because

1 times m-reduction [i] would yield (56, 86, 1733)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 108397 934152 713223 429216 568871 294025 851771 > 3⁸⁶ [i]