Here are two ways to construct the table.
The upper table strives for an open "look": no vertical lines and few but well-spaced horizontal lines. The reader's eyes are invited into the table and are free to roam around and take in all the information.
The lower table has an extremely closed look, mainly because of the overabundance of horizontal (8) and vertical (11) lines. It's not easy to move one's eyes from cell to cell.
It's up to you to decide which "look" works for you -- and, hopefully, for your readers as well. (Speaking for myself, I have a strong preference for the open look...)


\documentclass{article}
% Choose page parameters suitably:
\usepackage[letterpaper,margin=1in]{geometry}
\usepackage{array,booktabs}
\begin{document}
\[
%% First, the open "look"
\renewcommand\arraystretch{2.25}
\begin{array}{@{} l *{9}{>{\displaystyle}c} @{}}
\toprule
& \multicolumn{2}{c}{J^*(m)} & t^*(m)
& \multicolumn{2}{c}{J^{**}(m)} & t^{**}(m)
& \multicolumn{2}{c}{J^{***}(m)} & t^{***}(m) \\
\cmidrule(lr){2-3} \cmidrule(lr){5-6} \cmidrule(lr){8-9}
m & \frac{m-1}{m} & 2-\frac{m-1}{m} & m\pi
& \frac{m-3}{m} & 2-\frac{m-3}{m} & m\pi
& \frac{m-5}{m} & 2-\frac{m-5}{m} & m\pi \\
\midrule
1 & 0 & \frac{2}{1}=2 & \pi & & & & & & \\
2 & \frac{1}{2} & \frac{3}{2} & 2\pi & & & & & & \\
3 & \frac{2}{3} & \frac{3}{4} & 3\pi & & & & & & \\
4 & \frac{3}{4} & \frac{5}{4} & 4\pi & & & & & & \\
5 & \frac{4}{5} & \frac{6}{5} & 5\pi & & & & 0 & \frac{10}{5}=2 & 5\pi \\
\bottomrule
\end{array}
\]
\[
%% Second, the very closed "look"
\renewcommand\arraystretch{2}
\begin{array}{| l | *{9}{>{\displaystyle}c|} }
\hline
& \multicolumn{2}{c|}{J^*(m)} & t^*(m)
& \multicolumn{2}{c|}{J^{**}(m)} & t^{**}(m)
& \multicolumn{2}{c|}{J^{***}(m)} & t^{***}(m) \\
\hline
m & \frac{m-1}{m} & 2-\frac{m-1}{m} & m\pi
& \frac{m-3}{m} & 2-\frac{m-3}{m} & m\pi
& \frac{m-5}{m} & 2-\frac{m-5}{m} & m\pi \\
\hline
1 & 0 & \frac{2}{1}=2 & \pi & & & & & & \\
\hline
2 & \frac{1}{2} & \frac{3}{2} & 2\pi & & & & & & \\
\hline
3 & \frac{2}{3} & \frac{3}{4} & 3\pi & & & & & & \\
\hline
4 & \frac{3}{4} & \frac{5}{4} & 4\pi & & & & & & \\
\hline
5 & \frac{4}{5} & \frac{6}{5} & 5\pi & & & & 0 & \frac{10}{5}=2 & 5\pi\\
\hline
\end{array}
\]
\end{document}
Addendum to address @Sveinung's follow-up comment regarding desirable typographic features of the table: I fully agree with your observation that the second header row is currently too prominent, visually speaking; this is the case for both the "open" and the "closed" version. I didn't raise this issue in my initial answer because I had no idea if the OP's code, which contains lots of fraction terms, is for real or is meant as a mock-up. (One reason to believe it's mainly mock-up is that the information in columns 4, 7, and 10 is repeated verbatim.)
Assuming the fractional expressions in the second header row are for real, I can think of (at least!) 3 different, not mutually exclusive, approaches to improving the typography: (i) use a smaller font size for the entries in the second header row; (ii) switch from display-style to text-style fractions by using \tfrac instead of \frac; and (iii) use inline math notation; e.g., replace \frac{m-1}{m} and 2-\frac{m-1}{m} with 1-1/m and 1+1/m, respectively.
The third approach is implemented in the following table. Note that I've introduced inline-fraction notation not only in the header but in the body of the table as well.

\documentclass{article}
\usepackage[letterpaper,margin=1in]{geometry}
\usepackage{array,booktabs}
\begin{document}
\[
%% Third, a much more compact (but still "open") look
\begin{array}{@{} l *{9}{c} @{}}
\toprule
m & \multicolumn{2}{c}{J^*(m)} & t^*(m)
& \multicolumn{2}{c}{J^{**}(m)} & t^{**}(m)
& \multicolumn{2}{c}{J^{***}(m)} & t^{***}(m) \\
\cmidrule(lr){2-3} \cmidrule(lr){5-6} \cmidrule(lr){8-9}
& 1-1/m & 1+1/m & m\pi
& 1-3/m & 1+3/m & m\pi
& 1-5/m & 1+5/m & m\pi \\
\midrule
1 & 0 & 2 & \pi \\
2 & 1/2 & 3/2 & 2\pi \\
3 & 2/3 & 4/3 & 3\pi & 0 & 2 & 3\pi \\
4 & 3/4 & 5/4 & 4\pi & 1/4 & 7/4 & 4\pi \\
5 & 4/5 & 6/5 & 5\pi & 2/5 & 8/5 & 5\pi & 0 & 2 & 5\pi \\
\bottomrule
\end{array}
\]
\end{document}
Addendum, prompted by a follow-up question posted by the OP: To typeset the tabular material centered at the top of a page in a two-column document, you should encase all material from \[ to \] in a table* environment:
% ...
\begin{table*} % <-- new
\[
\begin{array}{@{} l *{9}{c} @{}}
\toprule
% (body of table)
\bottomrule
\end{array}
\]
\end{table*} % <-- new
% ... (remainder of document)
\begin{document} \begin{tabular}{|c|Sc|Sc|} \hline \backslashbox{a}{b} & \multicolumn{2}{c|}{c}\ \hline d & e & f\ \hline \end{tabular} \end{document}`
– leandriis Sep 05 '19 at 21:00