Some orthogonal arrays with 32 runs and their projection properties

Screening designs are useful for situations where a large number of factors are examined but only a few, k, of them are expected to be important. Traditionally orthogonal arrays such as Hadamard matrices and Plackett Burman designs have been studied for this purpose. It is therefore of practical interest for a given k to know all the classes of inequivalent projections of the design into the k dimensions that have certain statistical properties. In this paper we present 15 inequivalent Hadamard matrices of order n=32 constructed from circulant cores. We study their projection properties using several well-known statistical criteria and we provide minimum generalized aberration 2 level designs with 32 runs and up to seven factors that are embedded into these Hadamard matrices. A concept of generalized projectivity and design selection of such designs is also discussed.AMS Subject Classification: Primary 62K15, Secondary 05B20     

Projection Properties of Hadamard Matrices of Order 36 Obtained from Paley’s Constructions

In this paper we study the projection properties of 12 inequivalent Hadamard matrices of order 36 obtained from Paley’s constructions, using several statistical criteria. We also present generalized minimum aberration designs with 36 runs and up to 7 columns that are embedded into these Hadamard matrices.