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\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usetikzlibrary{arrows}
\usetikzlibrary{intersections}
\usetikzlibrary{math}
\usetikzlibrary{positioning}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{shapes.misc}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[
dot/.style = {
draw, circle, thick, black, fill = gray!40!white,
minimum size = 2mm,
inner sep = 0pt,
outer sep = 1mm,
},
]
\begin{scope}
\clip (-2,-2) rectangle (3,4);
\foreach \y in {-7,-6,...,7} {
\foreach \x in {-7,-6,...,7} {
\node[dot, xshift=3mm*\y] (N\x\y) at (\x, \y) {};
}
}
\end{scope}
\draw[black, thick] (-2, -2) rectangle (3,4);
\draw[red!80!black, thick, ->]
(N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
\draw[cyan!80!black, thick, ->]
(N00) to node[midway, left] {\(\vec{a}_2\)} (N01);
\end{tikzpicture}
\end{document}
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