Constructions of irredundant orthogonal arrays

An \begin{document}$ N \times k $\end{document} array id="M2">\begin{document}$ A with entries from id="M3">\begin{document}$ v $\end{document}-set id="M4">\begin{document}$ \mathcal{V} is said to be an orthogonal array id="M5">\begin{document}$ levels, strength id="M6">\begin{document}$ t and index id="M7">\begin{document}$ \lambda $\end{document}, denoted by OA\begin{document}$ (N,k,v,t) if every id="M9">\begin{document}$ N\times sub-array of id="M10">\begin{document}$ contains each id="M11">\begin{document}$ $\end{document}-tuple based on id="M12">\begin{document}$ exactly id="M13">\begin{document}$ times as a row. An id="M14">\begin{document}$ called irredundant, IrOA\begin{document}$ in any id="M16">\begin{document}$ (k-t ) sub-array, all its rows are different. Goyeneche id="M17">\begin{document}$ \dot{Z} $\end{document}yczkowski firstly introduced the definition IrOA showed that id="M18">\begin{document}$ corresponds id="M19">\begin{document}$ $\end{document}-uniform state id="M20">\begin{document}$ subsystems local dimension id="M21">\begin{document}$ (Physical Review A. 90 (2014), 022316). In this paper, we present some new constructions irredundant orthogonal arrays using difference matrices special over finite fields, respectively, consequence, many infinite families obtained. Furthermore, several classes id="M22">\begin{document}$ states arise these arrays.