Summary: A secret sharing scheme permits a secret to be shared among participants of an \(n\)-element group in such a way that only qualified subsets of participants can recover the secret. If any non-qualified subset has absolutely no information on the secret, then the scheme is called perfect. The share in a scheme is the information what a participant must remember. The author proves that for each \(n\) there exists an access structure on \(n\) participants so that any perfect sharing scheme must give some participant a share which is at least about \(n/\log n\) times the secret size. He also shows that the best possible result achievable by the information theoretic method used here is \(n\) times the secret size.
For the entire collection see [Zbl 0847.00061].