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The number oft-wise balanced designs

Authors:	Charles J Colbourn Dean G Hoffman Kevin T Phelps Vojtěch Rödl Peter M Winkler

Institution:	(1) Dept. of Combinatorics and Optimization, University of Waterloo, N2L 3G1 Waterloo, Ontario, CANADA;(2) Dept. of Alg., Combin. and Analysis, Auburn University, 36849-5307 Auburn, Alabama, U.S.A.;(3) Department of Mathematics, Emory University, 30322 Atlanta, Georgia, U.S.A.

Abstract:	We prove that the number oft-wise balanced designs of ordern is asymptotically $n\left( {(_t^n )/(t + 1)} \right)(1 + o(1))$ , provided that blocks of sizet are permitted. In the process, we prove that the number oft-profiles (multisets of block sizes) is bounded below by $\exp \left( {c_1 = \sqrt n \log n} \right)$ and above by $\exp \left( {c_2 = \sqrt n \log n} \right)$ for constants c₂>c₁>0.

Keywords:	05 B 30 05 B 05
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