  An important parameter in a secret sharing scheme is the number of minimal
qualified sets. Given this number, the universal access structure is the
richest possible structure, namely the one in which there are one or more
participants in every possible Boolean combination of the minimal qualified
sets. Every access structure is a substructure of the universal structure for
the same number of minimal qualified subsets, thus universal access structures
have the highest complexity given the number of minimal qualified sets. We show
that the complexity of the universal structure with $n$ minimal qualified sets
is between $n/\log_2 n$ and $n/2.7182$ asymptotically.
