Nonsymmetric configurations with line size k=4

The existence problem for nonsymmetric configurations with line size k = 4 will be discussed. It is conjectured that the obviously necessary existence conditions are also sufficient. New construction methods are discussed. The smallest unsettled case of such a configuration whose existence is now still in doubt is a structure with 92 points (instead of 56 points in an earlier paper). These configurations are equivalent to certain graphs and hypergraphs.