单纯正交表OA$_\lambda(3, 5, v)$的存在性

An orthogonal array of strength t,degree k,order v and index λ,denoted by OAλ(t,k,v),is a λvt× k array on a v symbol set such that each λvt× t subarray contains each t-tuple exactly λ times.An OAλ(t,k,v) is called simple and denoted by SOAλ(t,k,v)if it contains no repeated rows.In this paper,it is proved that the necessary conditions for the existence of an SOAλ(3,5,v) with λ≥ 2 are also sufficient with possible exceptions where v = 6 and λ∈ {3,7,11,13,15,17,19,21,23,25,29,33}.

Existence of Simple OA$_\lambda(3, 5, v)'$s

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 $\lambda \in \{3,7,11,13,15,17,19, 21,23,25,29,33\}$.