Gaps in the base set of primitive nonpowerful sign patterns

For a primitive nonpowerful square sign pattern A, the base of A, denoted by l(A), is the least positive integer l such that every entry of A l is #. In this article, we consider the base set of the primitive nonpowerful sign pattern matrices. Some useful results about the bases for the sign pattern matrices are presented there. Some special sign pattern matrices with given bases are characterized and more ‘gaps’ in the base set are shown.