1 The Existence of 2-SOLSSOMs -- 1 Introduction -- 2 Direct Constructions -- 3 Recursive Constructions -- 2 Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares -- 1 Introduction -- 2 Preliminaries -- 3 Direct Construction -- 4 Recursive Construction -- 5 A General Bound -- 6 The Case 2 ? n ? 6 -- 3 Combinatorial Trades: a Survey of Recent Results -- 1 Introduction and Preliminaries -- 2 Trades in designs -- 3 Trades in latin squares -- 4 Trade uses -- 5 Latin representations and trades used in tripartite decompositions -- 6 ?-way trades -- 7 Graphical trades -- 8 Future directions -- 4 Two-stage Generalized Simulated Annealing for the Construction of Change-Over Designs -- 1 Introduction -- 2 Notation and Definitions -- 3 A Two Stage Generalized Simulated Annealing Algorithm -- 4 Performance of the Two-Stage GSA -- 5 New Lower Bounds on the Maximum Number of Mutually Orthogonal Steiner Triple Systems -- 1 Introduction -- 2 Starters over Finite Fields -- 3 Automorphisms and Hill-climbing -- 4 Conclusion -- 6 On minimal defining sets in AG(d, 3) -- 1 Background -- 2 Introduction -- 3 Further Preliminaries -- 4 Proof of the Main Theorem -- 5 Sets of good hyperplanes in AG(d, 3) -- 6 Related critical sets -- 7 Appendix -- 7 Hadamard Matrices, Orthogonal designs and Construction Algorithms -- 1 Algorithms for constructing Hadamard matrices -- 2 On inequivalent Hadamard matrices -- 3 Algorithms for constructing orthogonal designs -- 4 Short amicable sets and Kharaghani type orthogonal designs -- 8 Constructing a Class of Designs with Proportional Balance -- 1 Proportionally balanced designs -- 2 The method of construction -- 3 Feasible parameters for ? = 2, 3 and 4 -- 4 Constructions motivated by Construction 5 -- 9 Constructions Using Balanced n-ary Designs -- 1 Introduction -- 2 Balanced n-ary Designs -- 3 Our Construction -- 4 Some Examples -- 5 Some Non-existence Results -- 6 An Improved Construction -- 7 Quadratic Residues -- 8 Another Improvement -- 9 An Application -- 10 More Difference Families -- 10 Sets of Steiner Triple Systems of Order 9 Revisited -- 1 Introduction -- 2 Large sets -- 3 Results -- 4 Uniformly intersecting sets -- 11 Solving Isomorphism Problems for t-Designs -- 1 Introduction -- 2 Basics -- 3 Moebius Inversions -- 4 Extensions of designs -- 12 Finding Double Youden Rectangles -- 1 Introduction -- 2 Definitions and Literature -- 3 Examples -- 4 Searching for a 13-cyclic 13 ? 40 DYR -- 5 Isomorphism -- 6 Further Properties of our new DYRs -- 7 Check for Balance -- 13 Kirkman Triple Systems and their Generalizations: A Survey -- 1 Introduction -- 2 Constructions for Kirkman Triple Systems and Nearly Kirkman Triple Systems for all admissible orders -- 3 Early Generalizations -- 4 Resolvable Packings and Coverings of v points where v ? 0 (mod 3) -- 5 Other Generalizations -- 6 Conclusion and Acknowledgements.