MinT - Best Known (26, 26+21, s)-Nets in Base 3

Best Known (26, 26+21, s)-Nets in Base 3

(26, 26+21, 40)-Net over F₃ — Constructive and digital

Digital (26, 47, 40)-net over F₃, using

1 times m-reduction [i] based on digital (26, 48, 40)-net over F₃, using
- trace code for nets [i] based on digital (2, 24, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]

(26, 26+21, 45)-Net over F₃ — Digital

Digital (26, 47, 45)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 26+21, 345)-Net in Base 3 — Upper bound on s

There is no (26, 47, 346)-net in base 3, because

1 times m-reduction [i] would yield (26, 46, 346)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9070 848027 319149 877941 > 3⁴⁶ [i]