k-circulant supersaturated designs

A class of supersaturated designs called k-circulant designs is explored. These designs are constructed from cyclic generators by cycling k elements at a time. The class of designs includes many Es-2-optimal designs, some of which are already known and some of which are more efficient than known designs for model estimation under factor sparsity. Generators for the most efficient designs are listed, and projection properties of some of the designs are explored. We also illustrate that some k-circulant supersaturated designs can be augmented with interaction columns to produce efficient designs for a larger number of factors or for estimating interactions.