## Design Theory |

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### Contents

1 BIBDs | 1 |

2 Symmetric BIBDs | 15 |

3 Resolvable BI BDs | 55 |

4 Orthogonal Latin Squares | 69 |

5 Pairwise Balanced Designs Group Divisible Designs | 97 |

6 Construction of Some Families of BI BDs | 117 |

7 tDesigns | 155 |

8 Steiner Systems | 177 |

9 Association Schemes and PBIBDs | 201 |

217 | |

219 | |

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### Common terms and phrases

0-th point 3-subsets abelian group affine resolvable association scheme assume base blocks BIBD bijective map Bruck-Ryser-Chowla Theorem called Clearly cogredient column conference matrix construction contained in exactly Corollary cyclic deduce define Definition denoted difference set difference triples disjoint distinct points elements equivalence class exactly one block Example 1.2 exist orthogonal latin finite affine plane finite projective plane Hadamard matrix Hence i-th associates idempotent incidence matrix integer inversive plane isomorphic l)-difference Lemma Let q Let X,B linear linear code matrix of order MOLS of order multiplication number of blocks obtain ordered pair orthogonal latin squares pair of distinct parallel classes parameter set permutation plane of order positive integer prime power proof of Theorem prove quasigroup rows of G SBIBD set of blocks set of points squares of order Steiner Systems Steiner triple system STS(v subsets subspace Suppose symmetric symmetric matrix t-design vector X)-BIBD