Using an exhaustive computer search on $v\leq 31$ points we obtain all $3$-$(v,\{4,6\},1)$ designs that have a transitive automorphism group and where the hexads are a symmetric design that is either a biplane, a semibiplane, or a partially balanced incomplete block design with two associate classes.

This is joint work with Michael Epstein and Spyros Magliveras.

Bio: Donald L. Kreher is an emeritus professor of Mathematical Sciences from Michigan Technological University, where he was a professor for 29 years. He co-authored with Douglas R. Stinson fifteen research papers and the internationally acclaimed textbook: "Combinatorial Algorithms: Generation Enumeration and Search". He has numerous other publications in computational and algebraic methods for determining the structure and existence of combinatorial configurations. In 1995, Professor Kreher was awarded the Marshall Hall Medal from the Institute of Combinatorics and its Applications. He is currently the production manager and editor-in-chief for the Bulletin of Combinatorics and its Applications (BICA).