Point-Cyclic Resolutions of 2-(64, 4, 1) Designs

A point-cyclic resolution of a 2-(v,k,1) design is invariant under a cyclic automorphism group of order v. Point-cyclic resolutions are of interest for their relations to many other combinatorial structures, and for their various applications. Resolutions of 2-(v,4,1) designs can exist if v≡4(mod 12). There are six point-cyclic resolutions of 2-(v,4,1) designs with v<64. Before the present study, v=64 was the smallest v for which neither theoretical nor constructive results on the existence of point-cyclic resolutions of 2-(v,4,1) designs were known. We establish that there are 258 point-cyclic resolutions of 2-(64,4,1) designs. The investigation is computer-aided.