  We estimate the size of a most loaded bin in the setting when the balls are
placed into the bins using a random linear function in a finite field. The
balls are chosen from a transformed interval. We show that in this setting the
expected load of the most loaded bins is constant.
  This is an interesting fact because using fully random hash functions with
the same class of input sets leads to an expectation of $\Theta\left(\frac{\log
m}{\log \log m}\right)$ balls in most loaded bins where $m$ is the number of
balls and bins.
  Although the family of the functions is quite common the size of largest bins
was not known even in this simple case.

Data Structures and Algorithms