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). 

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Abstract: 
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 $\lambda \in \{3,7,11,13,15,17,19, 21,23,25,29,33\}$. 
Citation: 
DOI:10.3770/j.issn:20952651.2015.03.004 
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