U-Type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes
Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53791#.VNMc1yzQrzE Author(s) Imane Rezgui 1 , Zebida Gheribi-Aoulmi 1 , Hervé Monod 2 Affiliation(s) 1 Department of Mathematics, University of Constantine 1, Constantine, Algeria . 2 INRA, UR MaIAGE, Jouy-en-Josas, Paris, France . ABSTRACT The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes ( m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns ( w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified u...