\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
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
$t-(\upsilon,\kappa,\lambda)$ design $(X,D)$ with minimum possible
value of $\lambda$, then there must be a
$t-(\upsilon,\kappa,\lambda)$ design $(X,D')$ such that $D \bigcap
D'=\O $.
\end{document}