Constructions Of Mosaics Of Combinatorial Designs

Mosaics of combinatorial designs were introduced first by Gnike,Greferath and Pavcevic in the article[9].As combinatorial designs have important applications in the design of experiment,mosaics are also widely used in the design of experiment.In ad-dition,mosaics have important applications in media access control[10]and distributed storage systems[15].Let c be a positive integer,and let(Xi,Bi)be a ti-(vi,ki,?i)design,i = 1,2,...,c,with the same number of points and blocks.A c-mosaic of designs B1,B2,...,Bc is a v × b matrix M =[mp,q],mp,q ?{1,2,...,c},for which holds that matrix Mi defined as is an incidence matrix of design Bi.So far,two constructions were given by making use of resolvable designs and the tiling of difference sets,in this paper,we make further research on constructions of mosaics of combinatorial designs.At first,we introduce an equivalent characterization of mosaics.Then,we give constructions of mosaics by making use of the combinatorial configurations such as near resolvable designs,quadruple systems,Steiner systems,difference sets,al-most difference sets,partitioned difference families,t-transitive groups,etc,and construct a batch of mosaics according to the known results of these combinatorial configurations.Partitioned difference families can be also used for the constructions of constant compo-sition codes.Finally,we construct several infinite classes of new partitioned difference families.