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Paper   IPM / M / 2359
School of Mathematics
  Title:   Some indecomposable t-designs
1.  G. B. Khosrovshahi
2.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: Des. Codes Cryptogr.
  Vol.:  32
  Year:  2004
  Pages:   235-238
  Supported by:  IPM
The existence of large sets of 5−(14,6,3) designs is in doubt. There are five simple 5−(14,6,6) designs known in the literature. In this note, by the use of a computer program, we show that all of these designs are indecomposable and therefore they do not lead to large sets os 5−(14,6,3) designs. Moreover, they provide the first counterexample for a conjecture on disjoint t-designs which states that if there exists a t−(υ,κ,λ) design (X,D) with minimum possible value of λ, then there must be a t−(υ,κ,λ) design (X,D′) such that DD′=Ø .

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