Perfect arrays with small phase alphabet

Perfect arrays are defined by having zero out-of-phase autocorrelation sidelobes. Such arrays find many applications, e.g. in two-dimensional synchronization techniques. With a known construction method, it is shown that perfect phase arrays can be obtained for every size. However, the phase alphabets of these constructed phase arrays increase by the size of the arrays. With further construction schemes the phase alphabet of perfect phase arrays can be reduced for particular sizes. Classes of perfect phase arrays are obtained whose phase alphabet does not increase with the size of the arrays