Uniformly Resolvable Three-wise Balanced Designs And Their Applications

t-wise balanced design is a important subject in combinatorial design theory and has been widely used in many areas.In this dissertation,we determine the spectrum of uniformly resolvable three-wise balanced designs with block sizes four and six,and use it to study the open problem posed by Hartman and Phelps in[26]:the existence of augmented resolvable Steiner quadruple systems and,the existence of(1,2)-resolvable Steiner quadruple systems.We almostly determined the existence of augmented resolvable Steiner quadruple systems and,give some infinite classes of(1,2)-resolvable Steiner quadruple systems.In chapter 2,we determine the spectrum of uniformly resolvable 3-wise balanced designs with block sizes four and six.In chapter 3,we give some constructions of augmented resolvable Steiner quadruple systems,specially,the tripling weight construction and the candelabra quadruple systems partner construction on augmented resolvable candelabra quadruple systems. We almostly solve the problem of the existence of augmented resolvable Steiner quadruple systems.Finally,we also present a possible approch to the settlement of the remeaining values.In chapter 4,we give some constructions of(1,2)-resolvable Steiner quadruple systems, specially,the tripling construction and the frame construction on(1,2)-resolvable candelabra quadruple systems.We give some infinite classes of(1,2)-resolvable Steiner quadruple systems.Finally,we also present a possible approch to solve Hartman and Phelps' open problem.