New classes of Kochen-Specker contextual sets

Finding Kochen-Specker contextual sets proves to be essential for quantum information and quantum computation in particular. It is therefore essential to find algorithms and programs which can generate arbitrary Kochen-Specker sets in a nearly-exhaustive manner. In this paper we present such generations for two new classes of Kochen-Specker sets. All sets from one of the classes are completely invisible to standard algorithms and programs from the literature as well as the upper part of sets from the second class. We also describe the methods and programs we used to obtain the sets on supercomputing clusters.