The asymptotic existence of group divisible designs of large order with index one

Abstract: This paper gives the answer to a question of R.M. Wilson regarding the existence of group divisible designs of large order. Let k and u be positive integers such that . Then there exists an integer such that there exists a group divisible design of group type with block size k and index one for any integer satisfying the necessary arithmetic conditions [1.] , [2.] . This paper also presents a large-index asymptotic existence theorem for group divisible t-designs with a fixed number of groups, fixed group size and fixed block size. [Copyright &y& Elsevier]