Improving two recursive constructions for covering arrays

Recursive constructions for covering arrays employ small ingredient covering arrays to build large ones. At present the most effective methods are "cut-and-paste" (or Roux-type) and column replacement techniques. Both can introduce substantial duplication of coverage; if unnecessary duplication can be avoided, then the recursion can yield a smaller array. Two extensions of covering arrays are introduced here for that purpose. The first examines arrays that cover only certain of the t-way interactions; we call these quilting arrays. We develop constructions of such arrays, and generalize column replacement techniques to use them in the construction of covering arrays. The second examines some consequences of nesting covering arrays of smaller strength in those of larger strength; the intersections among the covering arrays so nested lead to improvements in Roux-type constructions. For both directions, we examine consequences for the existence of covering arrays.