Constructing new covering arrays from LFSR sequences over finite fields

Let qq be a prime power and FqFq be the finite field with qq elements. A qq-ary m-sequence   is a linear recurrence sequence of elements from FqFq with the maximum possible period. A covering array  CA(N;t,k,v)CA(N;t,k,v)of strength  tt is a N×kN×k array with entries from an alphabet of size vv, with the property that any N×mN×m subarray has at least one row equal to every possible mm-tuple of the alphabet. The covering array number  CAN(t,k,v)CAN(t,k,v) is the minimum number NN such that a CA(N;t,k,v)CA(N;t,k,v) exists. Finding upper bounds for covering array numbers is one of the most important questions in this research area. Raaphorst, Moura and Stevens give a construction for covering arrays of strength 3 using m-sequences that improves upon some previous best bounds for covering array numbers. In this paper we introduce a method that generalizes this construction to strength greater than or equal to 4. Our implementation of this method returned new covering arrays and improved upon 38 previously best known covering array numbers. The new covering arrays are given here by listing the essential elements of their construction.