Covering perfect hash families and covering arrays of higher index

By exploiting symmetries of finite fields, covering perfect hash families provide a succinct representation for covering arrays of index one. For certain parameters, this connection has led to both the best current asymptotic existence results and the best known efficient construction algorithms for covering arrays. The connection generalizes in a straightforward manner to arrays in which every $t$-way interaction is covered $\lambda > 1$ times, i.e., to covering arrays of index more than one. Using this framework, we focus on easily computed, explicit upper bounds on numbers of rows for various parameters with higher index.