MinT - Best Known (58, 105, s)-Nets in Base 3

Best Known (58, 105, s)-Nets in Base 3

(58, 105, 64)-Net over F₃ — Constructive and digital

Digital (58, 105, 64)-net over F₃, using

1 times m-reduction [i] based on digital (58, 106, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 53, 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]

(58, 105, 80)-Net over F₃ — Digital

Digital (58, 105, 80)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 105, 655)-Net in Base 3 — Upper bound on s

There is no (58, 105, 656)-net in base 3, because

1 times m-reduction [i] would yield (58, 104, 656)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42 887125 665792 402595 279246 270387 340731 336188 448449 > 3¹⁰⁴ [i]