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Orthogonal arrays and t-designs are two of many combinatorial structures which have been found to be very useful in the statistical area of Experimental Design . Orthogonal arrays were introduced as suitable designs for planned experiments by [8] . Rao also gave key statistical properties for these arrays . On the other hand, the study of certain t-designs pre-dates the subject of Experimental Design which began in the 1920's . Now-a-days orthogonal arrays are used frequently in the design of quality control experiments largely due to the efforts of [10] . Moreover, 2-designs and 3-designs are used in all kinds of planned experiments including agricultural experiments. The practical utility of orthogonal arrays and t-designs has spurred research on these topics by both mathematicians and statisticians . The main objective of this paper is, therefore, to present constructions of certain classes of these combinatorial structures using Hadamard matrices as a tool. In first part of the paper we introduce the concept of an orthogonal array and in second part of the paper we use Hadamard matrices to construct arrays of strength 2 and strength 3 . In the third part of the paper motivates and then introduces the definition of t-designs . finally, we use Hadamard matrices to construct certain classes of these designs known as Hadamard 2- and 3- designs . Examples illustrating these constructions are also given.
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