Constructions and combinatorial problems in design of experiments
Complete sets of mutually orthogonal latin squares; Orthogonal arrays; Pairwise balandec designs and mutually orthogonal latin squares; General properties of incomplete block designs; Balanced incomplete block designs; Systems of distinct representatives and youden squares; Tactical configuration and doubly balanced designs; Partially balanced incomplet block designs; Graph theory and partial geometries; Duals of incomplete block designsMathematics for statisticians.
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Complete Sets of Mutually Orthogonal Latin Squares
of differences in the construction of orthogonal arrays 222 6 Orthogonal
Greatest lower bound on the number of mols of order s 100 43Ref
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additional weighings adjacency matrix affine a-resolvable Assn associate classes association scheme balanced incomplete block Bose Calcutta Stat Chapter characteristic roots column vector combinatorial confounded Corollary defined Definition denoted Difference set easily verify elements equations estimated existence factorial designs factorial experiments factors finite geometries following theorem group-divisible design Hadamard matrices Hence incidence matrix incomplete block designs integer interactions Kishen Kronecker product main effects Math method of constructing MOLS of order multiplicities necessary conditions nonsingular nonzero number of symbols obtained orthogonal array orthogonal latin squares pair pairwise balanced design parameters given partial geometry partially balanced arrays partially balanced incomplete PBIB pencil points prime power Proof prove the following Raghavarao result Sankhya satisfying Shrikhande singular weighing design strongly regular graph SUB arrangement symbol occurs symbols in common symmetrical BIB design Theorem treatment combinations triangular design variance vector space vertices Xu X2 zero