MinT - Best Known (48−22, 48, s)-Nets in Base 4

Best Known (48−22, 48, s)-Nets in Base 4

(48−22, 48, 66)-Net over F₄ — Constructive and digital

Digital (26, 48, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 24, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(48−22, 48, 684)-Net in Base 4 — Upper bound on s

There is no (26, 48, 685)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 79349 927750 383250 229889 655500 > 4⁴⁸ [i]