  What is the length of the shortest sequence $S$ of reals so that the set of
consecutive $n$-words in $S$ form a covering code for permutations on $\{1,2,
>..., n\}$ of radius $R$ ? (The distance between two $n$-words is the number of
transpositions needed to have the same order type.) The above problem can be
viewed as a special case of finding a De Bruijn covering code for a rooted
hypergraph. Each edge of a rooted hypergraph contains a special vertex, called
the {\it root} of the edge, and each vertex is the root of a unique edge,
called its {\it ball}. A De Bruijn covering code is a subset of the roots such
that every vertex is in some edge containing a chosen root. Under some mild
conditions, we obtain an upper bound for the shortest length of a De Bruijn
covering code of a rooted hypergraph, a bound which is within a factor of $\log
n$ of the lower bound.
