Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Combinatorics of finite sets -- 1.1. Fisher's Inequality -- 1.2. The First Ray-Chaudhuri-Wilson Inequality -- 1.3. Symmetric designs and Ryser designs -- 1.4. Equidistant families of sets -- Exercises -- Notes -- 2 Introduction to designs -- 2.1. Incidence structures -- 2.2. Graphs -- 2.3. Basic properties of (v, b, r, k, λ)-designs -- 2.4. Symmetric designs -- 2.5. The Bruck-Ryser-Chowla Theorem -- 2.6. Automorphisms of symmetric designs -- 2.7. A symmetric (41, 16, 6)-design -- 2.8. A symmetric (79, 13, 2)-design -- Exercises -- Notes -- 3 Vector spaces over finite fields -- 3.1. Finite fields -- 3.2. Affine planes and nets -- 3.3. The 36 officers problem -- 3.4. Projective planes -- 3.5. Affine geometries over finite fields -- 3.6. Projective geometries over finite fields -- 3.7. Combinatorial characterization of PG…(n, q) -- 3.8. Two infinite families of symmetric designs -- 3.9. Linear codes -- Exercises -- Notes -- 4 Hadamard matrices -- 4.1. Basic properties of Hadamard matrices -- 4.2. Kronecker product constructions -- 4.3. Conference matrices -- 4.4. Regular Hadamard matrices -- 4.5. From Paley matrices to regular Hadamard matrices -- 4.6. Regular sets of (±1)-matrices -- 4.7. Binary equidistant codes -- Exercises -- Notes -- 5 Resolvable designs -- 5.1. Bose's Inequality -- 5.2. Affine α-resolvable designs -- 5.3. Resolvable 2-designs -- 5.4. Embedding of resolvable designs in symmetric designs -- 5.5. Resolvable 2-designs and equidistant codes -- Exercises -- Notes -- 6 Symmetric designs and t-designs -- 6.1. Basic properties of t-designs -- 6.2. The Second Ray-Chaudhuri-Wilson Inequality -- 6.3. Hadamard 3-designs -- 6.4. Cameron's Theorem -- 6.5. Golay codes and Witt designs -- 6.6. Symmetric designs with parameters (56, 11, 2) and (176, 50, 14).

Exercises -- Notes -- 7 Symmetric designs and regular graphs -- 7.1. Strongly regular graphs -- 7.2. Eigenvalues of strongly regular graphs -- 7.3. Switching in strongly regular graphs -- 7.4. Symmetric designs with polarities -- 7.5. Symmetric designs and digraphs -- Exercises -- Notes -- 8 Block intersection structure of designs -- 8.1. Association schemes -- 8.2. Quasi-symmetric designs -- 8.3. Multiples of symmetric designs -- 8.4. Quasi-3 symmetric designs -- 8.5. Block schematic designs with three intersection numbers -- 8.6. Designs with a nearly affine decomposition -- 8.7. A symmetric (71, 15, 3)-design -- Exercises -- Notes -- 9 Difference sets -- 9.1. Group invariant matrices and group rings -- 9.2. Singer and Paley-Hadamard difference sets -- 9.3. Symmetries in a group ring -- 9.4. Building blocks and building sets -- 9.5. McFarland, Spence, and Davis-Jedwab difference sets -- 9.6. Relative difference sets -- Exercises -- Notes -- 10 Balanced generalized weighing matrices -- 10.1. Basic properties of BGW-matrices -- 10.2. BGW-matrices with classical parameters -- 10.3. BGW-matrices and relative difference sets -- 10.4. Kronecker product constructions -- 10.5. BGW-matrices and projective geometries -- Exercises -- Notes -- 11 Decomposable symmetric designs -- 11.1. A symmetric (66, 26, 10)-design -- 11.2. Global decomposition of symmetric designs -- 11.3. Six infinite families of globally decomposable symmetric designs -- 11.4. Productive Hadamard matrices -- 11.5. Symmetric designs with irregular global decomposition -- 11.6. Decomposable symmetric designs and regular graphs -- 11.7. Local decomposition of symmetric designs -- 11.8. Infinite families of locally decomposable symmetric designs -- 11.9. An infinite family of designs with a nearly affine decomposition -- Exercises -- Notes -- 12 Subdesigns of symmetric designs.

12.1. Tight subdesigns -- 12.2. Examples of tight subdesigns -- 12.3. Normal subdesigns -- 12.4. Symmetric designs with M-arcs -- Exercises -- Notes -- 13 Non-embeddable quasi-residual designs -- 13.1. Quasi-residuals of non-existing symmetric designs -- 13.2. Linear non-embeddability conditions -- 13.3. BGW-matrices and non-embeddability -- 13.4. Non-embeddable quasi-derived designs -- Exercises -- Notes -- 14 Ryser designs -- 14.1. Basic properties of Ryser designs -- 14.2. Type-1 Ryser designs -- 14.3. Ryser designs of prime index -- 14.4. Ryser designs of small index -- 14.5. Ryser designs of small gcd -- Exercises -- Notes -- Appendix -- References -- Index.