MinT - Best Known (26, 26+23, s)-Nets in Base 4

Best Known (26, 26+23, s)-Nets in Base 4

(26, 26+23, 48)-Net over F₄ — Constructive and digital

Digital (26, 49, 48)-net over F₄, using

1 times m-reduction [i] based on digital (26, 50, 48)-net over F₄, using
- trace code for nets [i] based on digital (1, 25, 24)-net over F₁₆, using
  - net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]

(26, 26+23, 59)-Net over F₄ — Digital

Digital (26, 49, 59)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 26+23, 684)-Net in Base 4 — Upper bound on s

There is no (26, 49, 685)-net in base 4, because

1 times m-reduction [i] would yield (26, 48, 685)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 79349 927750 383250 229889 655500 > 4⁴⁸ [i]