An existence theorem for group divisible designs of large order

  • Authors:

  • Hedvig Mohácsy;D. K. Ray-Chaudhuri

  • Affiliations:

  • Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio;Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2002

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Abstract

The following result gives a partial 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, 2 ≤ k ≤ u. Then there exists an integer m0 = m0(k,u) such that there exists a group divisible design of group type mu with block size k and index one for all integer m ≥ m0 if and only if (i) u-1 ≡ 0 mod(k-1), (ii) u(u-1) ≡ 0 mod k(k-1). This is a generalization of the well-known result of Chowla, Erdös, and Straus on the existence of transversal designs of large order.