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Pseudo New Modified Latin Square (NML m (m)) Type PBIB Designs
Authors:Davinder Kumar Garg
Institution:1. Department of Statistics , Punjabi University , Patiala, India dkgarg_stat@yahoo.co.in
Abstract:A New Modified Latin square NML i (m)] association scheme with i constraints for v = m 2 treatments was introduced by Garg (2008 Garg , D. K. ( 2008 ). New modified Latin square (NMLi) type PBIB designs . J. Math. Syst. Sci. 1 ( 4 ): 8389 . Google Scholar]). In this article, a new association scheme known as Pseudo New Modified Latin square Pseudo NML m (m)] type association scheme is defined. The parameters of Pseudo NML m (m) association scheme turned out to be parameters of NML i (m) association scheme by taking i = m in NML i (m) association scheme. The Pseudo NML m (m) association scheme will be the usual NML m (m) association scheme when m is a prime or a prime power. The PBIB designs following Pseudo NML m (m) association scheme will be called the Pseudo NML m (m) type PBIB designs. Analysis of Pseudo NML m (m) designs along with a construction method of these designs is also given in this article.
Keywords:Characteristic vectors  Mutually orthogonal  New modified latin square  Pseudo
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