Given a non-empty set S and a system F of functions defined on 5, the object of search is to detect an unknown element x in S, by observing the values of a sequence of test-functions / in F at x till there is enough information to detect x. The basic concepts and definitions of search theory were developed by Re'nyi [16,17]. He defined various types of homogeneities for the system F and discussed the duration of the process of random search.Strongly homogeneous systems of order two in two symbols are found to be closely related to the incidence matrix of equireplicated pairwise balanced designs. Some new systems of this type have been constructed here by using the incidence of subsets of points and ra-flats of finite geometries. Properties of weakly homogeneous binary systems of order two have been studied, and some new systems constructed using association matrices and Hadamard matrices. Two series of search systems possessing an optimality property have been also constructed.
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