Bounds for the Sizes of Components in Perfect Systems of Difference Sets

Abstract

Publisher Summary This chapter presents a study on bounds for the sizes of components in perfect systems of difference sets. Perfect systems of difference sets were introduced in connection with a problem of spacing antennas in radioastronomy. It is assumed that c, m, p 1 , . . . , p m be positive integers. It is said that the system { D l , .. . , D m } is a perfect system of difference sets for c . The number of components is at least proportional to the square of the size of the largest component. The number of perfect systems of difference sets starting with a given positive integer c , which have a given number of components, m , is finite. The chapter presents a parametric approach while estimating the size of the largest component and also estimates the average size of components.