MinT - Best Known (24, 24+13, s)-Nets in Base 3

Best Known (24, 24+13, s)-Nets in Base 3

(24, 24+13, 64)-Net over F₃ — Constructive and digital

Digital (24, 37, 64)-net over F₃, using

1 times m-reduction [i] based on digital (24, 38, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 19, 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]

(24, 24+13, 82)-Net over F₃ — Digital

Digital (24, 37, 82)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(24, 24+13, 1085)-Net in Base 3 — Upper bound on s

There is no (24, 37, 1086)-net in base 3, because

1 times m-reduction [i] would yield (24, 36, 1086)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 150301 107825 075621 > 3³⁶ [i]