| Preface | p. xi |
| The Existence of 2-SOLSSOMs | p. 1 |
| Introduction | p. 1 |
| Direct Constructions | p. 4 |
| Recursive Constructions | p. 8 |
| Conjugate Orthogonal Diagonal Latin Squares with Missing Subsquares | p. 23 |
| Introduction | p. 24 |
| Preliminaries | p. 27 |
| Direct Construction | p. 30 |
| Recursive Construction | p. 33 |
| A General Bound | p. 37 |
| The Case 2 [less than or equal] n [less than or equal] 6 | p. 41 |
| Combinatorial Trades: a Survey of Recent Results | p. 47 |
| Introduction and Preliminaries | p. 47 |
| Trades in designs | p. 48 |
| Trades in latin squares | p. 53 |
| Trade uses | p. 54 |
| Latin representations and trades used in tripartite decompositions | p. 56 |
| [mu]-way trades | p. 58 |
| Graphical trades | p. 60 |
| Future directions | p. 62 |
| Two-stage Generalized Simulated Annealing for the Construction of Change-Over Designs | p. 69 |
| Introduction | p. 69 |
| Notation and Definitions | p. 71 |
| A Two Stage Generalized Simulated Annealing Algorithm | p. 73 |
| Performance of the Two-Stage GSA | p. 75 |
| New Lower Bounds on the Maximum Number of Mutually Orthogonal Steiner Triple Systems | p. 81 |
| Introduction | p. 81 |
| Starters over Finite Fields | p. 83 |
| Automorphisms and Hill-climbing | p. 92 |
| Conclusion | p. 99 |
| On minimal defining sets in AG(d, 3) | p. 103 |
| Background | p. 104 |
| Introduction | p. 105 |
| Further Preliminaries | p. 116 |
| Proof of the Main Theorem | p. 121 |
| Sets of good hyperplanes in AG(d, 3) | p. 124 |
| Related critical sets | p. 127 |
| Appendix | p. 129 |
| Hadamard Matrices, Orthogonal designs and Construction Algorithms | p. 133 |
| Algorithms for constructing Hadamard matrices | p. 134 |
| On inequivalent Hadamard matrices | p. 163 |
| Algorithms for constructing orthogonal designs | p. 176 |
| Short amicable sets and Kharaghani type orthogonal designs | p. 193 |
| Constructing a Class of Designs with Proportional Balance | p. 207 |
| Proportionally balanced designs | p. 208 |
| The method of construction | p. 211 |
| Feasible parameters for [alpha] = 2, 3 and 4 | p. 214 |
| Constructions motivated by Construction 5 | p. 218 |
| Constructions Using Balanced n-ary Designs | p. 227 |
| Introduction | p. 227 |
| Balanced n-ary Designs | p. 229 |
| Our Construction | p. 230 |
| Some Examples | p. 232 |
| Some Non-existence Results | p. 235 |
| An Improved Construction | p. 238 |
| Quadratic Residues | p. 240 |
| Another Improvement | p. 243 |
| An Application | p. 246 |
| More Difference Families | p. 247 |
| Sets of Steiner Triple Systems of Order 9 Revisited | p. 255 |
| Introduction | p. 255 |
| Large sets | p. 257 |
| Results | p. 260 |
| Uniformly intersecting sets | p. 263 |
| Solving Isomorphism Problems for t-Designs | p. 277 |
| Introduction | p. 277 |
| Basics | p. 279 |
| Moebius Inversions | p. 282 |
| Extensions of designs | p. 293 |
| Finding Double Youden Rectangles | p. 301 |
| Introduction | p. 301 |
| Definitions and Literature | p. 302 |
| Examples | p. 302 |
| Searching for a 13-cyclic 13 X 40 DYR | p. 306 |
| Isomorphism | p. 309 |
| Further Properties of our new DYRs | p. 313 |
| Check for Balance | p. 314 |
| Kirkman Triple Systems and their Generalizations: A Survey | p. 317 |
| Introduction | p. 318 |
| Constructions for Kirkman Triple Systems and Nearly Kirkman Triple Systems for all admissible orders | p. 334 |
| Early Generalizations | p. 342 |
| Resolvable Packings and Coverings of v points where v [not identical with] 0 (mod 3) | p. 348 |
| Other Generalizations | p. 359 |
| Conclusion and Acknowledgements | p. 363 |
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