  The optimal packings of n unit discs in the plane are known for those natural
numbers n, which satisfy certain number theoretic conditions. Their geometric
realizations are the extremal Groemer packings (or Wegner packings). But an
extremal Groemer packing of n unit discs does not exist for all natural numbers
n and in this case, the number n is called exceptional. We are interested in
number theoretic characterizations of the exceptional numbers. A counterexample
is given to a conjecture of Wegner concerning such a characterization. We
further give a characterization of the exceptional numbers, whose shape is
closely related to that of Wegner's conjecture.
