The topic of this research project are constructions of combinatorial objects with additional algebraic structure, such as quasi-symmetric designs, schematic designs, q-analogs of designs, difference sets, (semi)partial geometries, and generalisations. Results in algebraic combinatorics impose restrictions on the parameters and properties of such objects that can be exploited to narrow-down the search space and develop specialised algorithms for their construction and classification.

Research objectives

• Development of algorithmic methods for the construction and classification of combinatorial objects with strong algebraic structure. These methods utilise known algebraic and combinatorial properties of the objects to handle larger parameters and problems that have been out of reach with traditional construction methods.
  
  
• Widening of theoretical knowledge about combinatorial objects that are the topic of research. Interesting theorems are often discovered and proved on the basis of available examples. It is expected that the results of the project will lead to such discoveries.
  
  
• Development of a software package, implemented in GAP, for the construction and analysis of combinatorial objects.