[Tex/LaTex] How to add vertical space before `hline` in `array`

Question

I am trying to format the following table with more space below the horizontal lines.

\begin{equation*}
    \begin{array}{|c|c|c|}
        \hline
        i & (266)_i & [266]_i\\[3pt]
        \hline
        1   & 2^{2^{2+1}} + 2^{2+1} + 2 &   \omega^{\omega^{\omega+1}} + \omega^{\omega+1} + \omega                 \\
        2   & 3^{3^{3+1}} + 3^{3+1} + 2 &   \omega^{\omega^{\omega+1}} + \omega^{\omega+1} + 2                  \\
        3   & 4^{4^{4+1}} + 4^{4+1} + 1 &   \omega^{\omega^{\omega+1}} + \omega^{\omega+1} + 1                  \\
        4   & 5^{5^{5+1}} + 5^{5+1}     &   \omega^{\omega^{\omega+1}} + \omega^{\omega+1}                      \\
        5   & 3^{3^{3+1}} + 3^{3+1} + 2 &   3^{3^{3+1}} + 3^{3+1} + 2                   \\
        \vdots & \vdots & \vdots        \\
        \hline
    \end{array}
\end{equation*}

I have tried replacing hline by \hline\noalign{\vskip 3pt} but this leaves a vertical break in the borders {|c|c|c|}.

Answer 1

A simple solution based on the cellspace package, which defines minimal vertical spacing at the top or bottom of cells in columns with qualifier prefixed with the letter S:

    \documentclass{article}
    \usepackage{array, amsmath}

\usepackage[math]{cellspace}
\setlength\cellspacetoplimit{3pt}
\setlength\cellspacebottomlimit{3pt}
    \begin{document}

\begin{equation*}
    \begin{array}{|Sc|>{$}Sc<{$}|c|}
        \hline
 i & (266)_i & [266]_i\\
        \hline
        1 & 2^{2^{2+1}} + 2^{2+1} + 2 & \omega^{\omega^{\omega+1}} + \omega^{\omega+1} + \omega \\
        2 & 3^{3^{3+1}} + 3^{3+1} + 2 & \omega^{\omega^{\omega+1}} + \omega^{\omega+1} + 2 \\
        3 & 4^{4^{4+1}} + 4^{4+1} + 1 & \omega^{\omega^{\omega+1}} + \omega^{\omega+1} + 1 \\
        4 & 5^{5^{5+1}} + 5^{5+1} & \omega^{\omega^{\omega+1}} + \omega^{\omega+1} \\
        5 & 3^{3^{3+1}} + 3^{3+1} + 2 & 3^{3^{3+1}} + 3^{3+1} + 2 \\[-6pt]
        \vdots & \vdots & \vdots \\
        \hline
    \end{array}
\end{equation*}

    \end{document}