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Paper   IPM / M / 771
School of Mathematics
  Title:   Some results on the existence of large sets of t-designs
1.  G. B. Khosrovshahi
2.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: J. Combin. Des.
  Vol.:  11
  Year:  2003
  Pages:   144-151
  Supported by:  IPM
A set of trivial necessary conditions for the existence of a large set of t-designs, LS[N](t,k,v), is N|((vi) || (ki)) for i=0,…, t. There are two conjectures due to Hartman and Khosrovshahi which state that the trivial necessary conditions are sufficient in the cases N=2 and 3, respectively. Ajoodani-Namini has established the truth of Hartman's conjecture for t=2. Apart from this celebrated result, we know the correctness of the conjectures for a few small values of k, when N=2 and t ≤ 6, and also when N=3 and t ≤ 4. In this article, we show that the foregoing results are in fact true for infinitely many values of k.

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