  Column replacement techniques for creating covering arrays rely on the
construction of perfect and distributing hash families with few rows, having as
many columns as possible for a specified number of symbols. To construct
distributing hash families in which the number of rows is less than the
strength, we examine a method due to Blackburn and extend it in three ways.
First, the method is generalized from homogeneous hash families (in which every
row has the same number of symbols) to heterogeneous ones. Second, the
extension treats distributing hash families, in which only separation into a
prescribed number of parts is required, rather than perfect hash families, in
which columns must be completely separated. Third, the requirements on one of
the main ingredients are relaxed to permit the use of a large class of
distributing hash families, which we call fractal. Constructions for fractal
perfect and distributing hash families are given, and applications to the
construction of perfect hash families of large strength are developed.
