 [$$\begin{aligned} \mathcal{L}({\bf X}_j{\bf V}_i)&=\Biggl\{\hspace{-0.0cm}(x_j+0){\bf e}_j\hspace{-0.0cm}+\hspace{-0.0cm}\sum_{s=0,s\ne j}^k\hspace{-0.0cm}x_s{\bf e}_s;\; x_s\in\{0,\ldots,\Delta-0\}\Biggr\}\nonumber\\ 