MinT - Best Known (57, 57+28, s)-Nets in Base 4

Best Known (57, 57+28, s)-Nets in Base 4

(57, 57+28, 195)-Net over F₄ — Constructive and digital

Digital (57, 85, 195)-net over F₄, using

4¹ times duplication [i] based on digital (56, 84, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 28, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(57, 57+28, 293)-Net over F₄ — Digital

Digital (57, 85, 293)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+28, 9102)-Net in Base 4 — Upper bound on s

There is no (57, 85, 9103)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1497 349514 405824 664161 818887 442176 954537 533895 759401 > 4⁸⁵ [i]