New skew Hadamard matrices and their application in edge designs

摘要

When a large number of variables (factors) are examined in experimental situation it is often anticipated that only few of these will be important. Usually it is not known which of the variables will be the important ones, so it is not known which columns of the experimental design will be of further interest. Many designs have been proposed to be used for screening experiments and to identify the relevant variables. Recently Elster and Neumaier (1995) introduced a new class of experimental designs called edge designs. These designs allow a model-independent estimate of the set of relevant variables, thus providing more robustness than traditional designs. Among others they proposed a construction for edge designs with n- 1 edges, n = 0 (mod 4) from skew Hadamard matrices of order n. In this paper we use an algorithm to find four (1,-1) matrices A, B, C, D of order 11, satisfying the relation AAT + BBT + CGT + DDT - 44/u, where A is of skew type. We then use them in the Goethals-Seidel array to obtain new skew Hadamard matrices of order 44. These matrices can be used for the construction of new edge designs with 43 variables and 43 edges. An illustrative simulated example using an edge design in 86 runs is also presented.