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Paper   IPM / M / 739
School of Mathematics
  Title:   Root cases of large sets of t-designs
  Author(s): 
1.  G. B. Khosrovshahi
2.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: Discrete Math.
  Vol.:  263
  Year:  2003
  Pages:   143-155
  Supported by:  IPM
  Abstract:
A large set of t-(v,k,λ) designs of size N, denoted by LS[N](t,k,v), is a partition of all k-subsets of a v-set into N disjoint t-(v,k,λ) designs, where N=((vt) || (kt))/λ. A set of trivial necessary conditions for the existence of an LS[N](t,k,v) is N| ((vi) || (ki)) for i=0,...,t. In this paper we extend some of the recursive methods for constructing large sets of t-designs of prime sizes. By utilizing these methods we show that for the construction of all possible large sets with the given N, t, and k, it suffices to construct a finite number of large sets which we call root cases. As a result, we show that the trivial necessary conditions for the existence of LS[3](2,k,v) are sufficient for k ≤ 80.

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