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

Authors:
Hedvig Mohácsy
Affiliations:
Arizona State University, Department of Mathematics and Statistics, Tempe, AZ, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

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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 2==m"0 satisfying the necessary arithmetic conditions1.m(u-1)=0mod(k-1), 2.m^2u(u-1)=0modk(k-1). 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.