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1．BIBDs 1

1.1 Definition and Fundamental Properties of BIBDs 1

1.2 Isomorphisms and Automorphisms 8

1.3 Constructions of New BIBDs from Old Ones 12

1.4 Exercises 14

2．Symmetric BIBDs 15

2.1 Definition and Fundamental Properties 15

2.2 Bruck-Ryser-Chowla Theorem 21

2.3 Finite Projective Planes as Symmetric BIBDs 26

2.4 Difference Sets and Symmetric BIBDs 30

2.5 Hadamard Matrices and Symmetric BIBDs 43

2.6 Derived and Residual BIBDs 51

2.7 Exercises 52

3．Resolvable BIBDs 55

3.1 Definitions and Examples 55

3.2 Finite Affine Planes 57

3.3 Properties of Resolvable BIBDs 61

3.4 Exercises 67

4．Orthogonal Latin Squares 69

4.1 Orthogonal Latin Squares 69

4.2 Mutually Orthogonal Latin Squares 74

4.3 Singular Direct Product of Latin Squares 79

4.4 Sum Composition of Latin Squares 84

4.5 Orthogonal Arrays 89

4.6 Transversal Designs 92

4.7 Exercises 95

5．Pairwise Balanced Designs;Group Divisible Designs 97

5.1 Pairwise Balanced Designs 97

5.2 Group Divisible Designs 106

5.3 Closedness of Some Sets of Positive Integers 111

5.4 Exercises 115

6．Construction of Some Families of BIBDs 117

6.1 Steiner Triple Systems 117

6.2 Cyclic Steiner Triple Systems 123

6.3 Kirkman Triple Systems 131

6.4 Triple Systems 142

6.5 Biplanes 147

6.6 Exercises 153

7．t-Designs 155

7.1 Definition and Fundamental Properties of t-Designs 155

7.2 Restriction and Extension 162

7.3 Extendable SBIBDs and Hadamard 3-Designs 166

7.4 Finite Inversive Planes 173

7.5 Exercises 176

8．Steiner Systems 177

8.1 Steiner Systems 177

8.2 Some Designs from Hadamard 2-Designs and 3-Designs 179

8.3 Steiner Systems S(4;11,5)and S(5;12,6) 185

8.4 Binary Codes 191

8.5 Binary Golay Codes and Steiner Systems S(4;23,7)and S(5;24,8) 196

8.6 Exercises 200

9．Association Schemes and PBIBDs 201

9.1 Association Schemes 201

9.2 PBIBDs 206

9.3 Association Schemes(Continued) 207

9.4 Exercises 216

References 217

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