"Make it explicit!" is my favorite slogan when searching for combinatorial designs. My main goal is to construct them explicitly, i.e., to give a complete recipe for their realization even when they are known to exist. This might appear a bit old-fashioned considering the recent explosion of non-constructive asymptotic results obtained via probabilistic methods. Even though these achievements are truly very impressive we have to admit that, for now, they cannot be used for applications. Also, the complete recipe is more easily reachable by imposing many symmetries so that the resulting design will be intrinsically "beautiful". A recent success in this direction was the explicit construction of "nearly transitive" Kirkman triple systems whose orders fill some congruence classes. Yet, in spite of my "dogma", I had sometimes to raise the white flag and be content with "almost complete" recipes. I will select some constructions for combinatorial designs illustrating what kind of difficulties one deals with to make them explicit.

S. Bonvicini, M. Buratti, M. Garonzi, G. Rinaldi, T. Traetta, The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class, Designs, Codes and Cryptography 89 (2021) 2725-2757.

Bio: Marco Buratti received a Math degree in 1985 at the University "La Sapienza" of Rome. He is currently a Full Professor of Geometry at the University of Perugia. His area of research is Combinatorial Designs. He received the "Hall Medal" from the Institute of Combinatorics and its Applications in 1998. He is an Editorial member of seven journals in Combinatorics. In particular, he is an EiC of the Bulletin of the Institute of Combinatorics and its Applications. He has kept a column about palindromes on "Il Sole 24 ore" since 2005; he is a national candidate chess master since 1984.