We tabulate polynomials in Z[t] with a given factorization partition, bad
reduction entirely within a given set of primes, and satisfying auxiliary
conditions associated to 0, 1, and infinity. We explain how these sets of
polynomials are of particular interest because of their role in the
construction of nonsolvable number fields of arbitrarily large degree and
bounded ramification. Finally we discuss the similar but technically more
complicated tabulation problem corresponding to removing the auxiliary
conditions.Comment: 26 pages, 3 figure
