MinT - Best Known (56, 56+41, s)-Nets in Base 3

Best Known (56, 56+41, s)-Nets in Base 3

(56, 56+41, 72)-Net over F₃ — Constructive and digital

Digital (56, 97, 72)-net over F₃, using

1 times m-reduction [i] based on digital (56, 98, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 49, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]

(56, 56+41, 88)-Net over F₃ — Digital

Digital (56, 97, 88)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+41, 790)-Net in Base 3 — Upper bound on s

There is no (56, 97, 791)-net in base 3, because

1 times m-reduction [i] would yield (56, 96, 791)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6418 864685 471850 296892 418275 935737 909789 222233 > 3⁹⁶ [i]