A covering array of strength $t$ on $v$ symbols is an array with the property that, for every $t$-combination of column vectors, every one of the $v^t$ possible $t$-tuples of symbols appears as a row at least once in the sub-array defined by these column vectors.

Arrays whose rows are cyclic shifts of an m-sequence over a finite field possess many combinatorial properties and have been used to construct various combinatorial objects; see the recent survey by Moura, Mullen and Panario (2016). Inspired by the work of Colbourn (2010), we construct covering arrays by applying character sums over finite fields to the cyclic shifts of an m-sequence. Taking advantage of the balanced way in which the m-sequence elements are distributed, we are able to evaluate these sums and describe new infinite families of covering arrays of arbitrary strength.

Joint work with Lucia Moura, Daniel Panario, and Brett Stevens.