## Design TheoryThis book deals with the basic subjects of design theory. It begins with balanced incomplete block designs, various constructions of which are described in ample detail. In particular, finite projective and affine planes, difference sets and Hadamard matrices, as tools to construct balanced incomplete block designs, are included. Orthogonal latin squares are also treated in detail. Zhu's simpler proof of the falsity of Euler's conjecture is included. The construction of some classes of balanced incomplete block designs, such as Steiner triple systems and Kirkman triple systems, are also given. T-designs and partially balanced incomplete block designs (together with association schemes), as generalizations of balanced incomplete block designs, are included. Some coding theory related to Steiner triple systems are clearly explained. The book is written in a lucid style and is algebraic in nature. It can be used as a text or a reference book for graduate students and researchers in combinatorics and applied mathematics. It is also suitable for self-study. |

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0-th point 3-subsets abelian group affine resolvable association scheme assume AutW(A base blocks BIBDs bijective map biplane Bruck-Ryser-Chowla Theorem called Clearly cogredient column conference matrix construction contained in exactly Corollary cyclic deduce define Definition denoted difference set difference triples distinct points elements Example 1.2 exist orthogonal latin finite affine plane finite projective plane GD(v Hadamard 2-design Hadamard matrix Hence Hussian graphs i-th associates idempotent incidence matrix integer inversive plane isomorphic l)-difference set Lemma Let q Let X,B linear 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