The Asymptotic Existence of Group Divisible t-Designs of Large Order with Index One
Article first published online: 18 JUL 2013
© 2013 Wiley Periodicals, Inc.
Journal of Combinatorial Designs
Volume 21, Issue 12, pages 541–562, December 2013
How to Cite
Mohácsy, H. (2013), The Asymptotic Existence of Group Divisible t-Designs of Large Order with Index One. J. Combin. Designs, 21: 541–562. doi: 10.1002/jcd.21365
- Issue published online: 2 OCT 2013
- Article first published online: 18 JUL 2013
- Manuscript Revised: 13 JUN 2013
- Manuscript Received: 22 MAY 2012
- group divisible t-designs;
- transversal designs;
- asymptotic existence
The following result gives the answer to the question of whether for a fixed number of groups u and fixed block size k a group divisible t-design of group type with block size k and index one exists for sufficiently large m if the necessary arithmetic conditions are satisfied. Let k and u be positive integers, . Then there exists an integer such that there exists a group divisible t-design of group type with block size k and index one for any integer satisfying the necessary arithmetic conditions
The case of this theorem gives an existence theorem for transversal t-designs of large order, which was previously proved by J. L. Blanchard in an unpublished manuscript.