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TIGHT ASYMMETRIC ORTHOGONAL ARRAYS OF STRENGTH 2 USING FINITE PROJECTIVE GEOMETRY
M. L. AGGARWAL,LIH-YUAN DENG,MUKTA D. AZUMDER 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.1
Wu et al:(1992) constructed some general classes of tight asymmetricet al:(2002) obtained asymmetric orthogonal arrays of strength 2 using the con-cept of mixed spread in nite projective geometry. In this paper, we obtainsome new tight asymmetric orthogonal arrays of strength 2 using the conceptof mixed partition in nite projective geometry.AMS 2000 subject classications.Primary 62K15; Secondary 05B15.Keywords.Tight asymmetric orthogonal array, mixed spread, mixed partition, ats.1. IntroductionRao (1973) introduced asymmetric orthogonal arrays which have found nu-merous applications for quality improvements in the context of the industrialexperiments as pointed out by Taguchi (1987). An asymmetric orthogonal ar-ray OA(N;k;mk11 mk22 mknn ;t N k where k =k1 + k2 + + kn is the total number of factors in whichk1 columns have m1symbols ranging fromf0;1;:;m 1 1g, the nextk2 columns have m2 sym-bols ranging fromf0;1;:;m 2 1g and so on with the property that in anyN t subarray every possiblet row. An OA(N;k;mk11 mk22 mknn ;2) attaining Rao's boundN 1 +k1(m1 1) + k2(m2 1) + + kn(mn 1) is called tight. The special casem1 = m2 = = mn = m, (say) corresponds to a symmetric orthogonal array,denoted by an OA( ).Received August 2004; accepted February 2006.1Corresponding author. Department of Mathematical Sciences, The University of Memphis,Memphis, TN 38152, USA (e-mail : maggarwl@memphis.edu)