MinT - Best Known (54, 54+43, s)-Nets in Base 3

Best Known (54, 54+43, s)-Nets in Base 3

(54, 54+43, 64)-Net over F₃ — Constructive and digital

Digital (54, 97, 64)-net over F₃, using

1 times m-reduction [i] based on digital (54, 98, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 49, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]

(54, 54+43, 77)-Net over F₃ — Digital

Digital (54, 97, 77)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+43, 638)-Net in Base 3 — Upper bound on s

There is no (54, 97, 639)-net in base 3, because

1 times m-reduction [i] would yield (54, 96, 639)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6503 831385 551465 554108 652244 412938 935678 980311 > 3⁹⁶ [i]