Some Structural.Characterizations of \(\lambda\)-Designs

The twenty-five year old \(\lambda\)-design conjecture remains unsettled. Attempts to characterize these irregular, tight, \(2\)-designs have produced a great number of parametric and dual structure characterizations of the so-called Type-I Designs. We establish some new structural characterizations and establish the conjecture in the smallest unsettled case (\(\lambda = 14\)) of the \(2p\) family.