On symmetric designs with parameters \((176, 50, 14)\)
Let \(H= (Z_4\times Z_4\times Z_4)\cdot F_{21}\), where \(F_{21}\) is the Frobenius group of order 21, operate on a symmetric \((176, 50, 14)\) design resulting in two orbits of lengths 64 and 112 (with stabilizers isomorphic to \(F_{21}\) and \(Z_{12}\), respectively). \(H\) is a second-maximal subgroup of the Higman-Sims simple group \(G\) of order 44,352,000. The author establishes that there exist precisely two such designs: the Graham-Higman design whose full automorphism group is \(G\) and a new design whose full automorphism group is \(H\). Both designs are self-dual. Base blocks are provided for both designs.
scientific article; zbMATH DE number 823500