MinT - Best Known (54−26, 54, s)-Nets in Base 4

Best Known (54−26, 54, s)-Nets in Base 4

(54−26, 54, 48)-Net over F₄ — Constructive and digital

Digital (28, 54, 48)-net over F₄, using

trace code for nets [i] based on digital (1, 27, 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]

(54−26, 54, 57)-Net over F₄ — Digital

Digital (28, 54, 57)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−26, 54, 588)-Net in Base 4 — Upper bound on s

There is no (28, 54, 589)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 329 106209 357584 040831 458297 322836 > 4⁵⁴ [i]