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| Paper IPM / M / 2359 |
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| Abstract: | |||||
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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 D ∩D′=Ø .
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