I proved, that if the answer exists - we can use no more than 931=(50-1)(20-1) frames. I mean, that if we use more than 931 frames - some frame will be fully covered with others. :)
  The bound is precise - of course, if the author's covering is not necessarily with no more than 15 frames.
  It is an interesting mathematical problem, so someone could try to solve it! :)