We describe a very versatile, fast and useful open source software package to compute combinatorial objects up to isomorphism called Orbiter. We provide an overview of some of the design decisions made during development, and we point out similar software packages. We discuss ways in which combinatorial data can be computed, analyzed and permanently stored for later use. This paper expands on earlier work published in [8].

In Finite Geometry, a class of objects known as BLT-sets play an important role. They are points on the Q(4,q) quadric satisfying a condition on triples. This paper is a contribution to the difficult problem of classifying these sets up to isomorphism, i.e., up to the action of the automorphism group of the quadric. We reduce the classification problem of these sets to the problem of classifying rainbow cliques in graphs. This allows us to classify BLT-sets for all orders q in the range 31 to 67.