Enumeration and Isomorphism for 1-Factorisations and Latin squares

This thesis develops algorithms for generating various two-dimensional patterns in an area known as combinatorial design theory. These algorithms are used to compile catalogues of previously unclassified designs with certain parameters. A better understanding of which substructures are likely to be present provides provably more efficient tests for detecting structural similarities. The designs studied in this work have been proposed for use in a wide range of applications including scheduling, cryptography and protocols for fault-tolerant data storage.