Non-trivial t-designs without repeated blocks exist for all t

A computer package is being developed at Bayreuth for the generation and investigation of discrete structures. The package is a C and C++ class library of powerful algorithms endowed with some graphical interface modules. Some standard applications can be run automatically whereas research projects mostly require small C or C++ programs. The basic philosophy behind the system is to transform problems into standard problems of e.g. group theory, graph theory, linear algebra, graphics, or databases and use highly specialized routines from that field to tackle the problems. The transformations required often follow the same principles especially in questions about generation and isomorphism testing. We therefore explain some of this background. We relate orbit problems to double cosets and offer a way to solve double coset problems in many important cases. Since the graph isomorphism problem is equivalent to some double coset problem, no polynomial algorithm can be expected in general. Bu...

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Luc Teirlinck
• Keywords: C++ Class Library, DM 2006, Double Coset Problem, Graphical Interface Modules