Existence of Simple OA$_\lambda(3, 5, v)'$s
Received:May 19, 2014  Revised:March 04, 2015
Key Words: orthogonal arrays   simple   construction   existence  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11301342; 11226282) and Shanghai Special Research Fund for Training College's Young Teachers (Grant No.ZZlx13001).
Author NameAffiliation
Ce SHI School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, P. R. China 
Ling JIANG Department of Mathematics, Soochow University, Jiangsu 215006, P. R. China 
Bin WEN School of Mathematics and Statistics, Changshu Institute of Technology, Jiangsu 215500, P. R. China 
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      An orthogonal array of strength $t$, degree $k$, order $v$ and index $\lambda$, denoted by OA$_\lambda(t,k,v)$, is a $\lambda v^t\times k$ array on a $v$ symbol set such that each $\lambda v^t\times t$ subarray contains each $t$-tuple exactly $\lambda$ times. An OA$_\lambda(t,k,v)$ is called simple and denoted by SOA$_\lambda(t,k,v)$ if it contains no repeated rows. In this paper, it is proved that the necessary conditions for the existence of an SOA$_\lambda(3,5,v)$ with $\lambda \geq 2$ are also sufficient with possible exceptions where $v=6$ and $\lambda \in \{3,7,11,13,15,17,19, 21,23,25,29,33\}$.
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