(4) 8 singers participate in the arts festival, preparing to arrange $m$ performances, each time 4 of them will perform on stage, requiring that any two of the 8 singers perform together the same number of times. Please design a scheme so that the number of performances $m$ is the least.
Let any two singers perform together $r$ times, then we have
$$
\begin{aligned}
6 m=m \mathrm{C}_{4}^{2} & =r \mathrm{C}_{8}^{2}=28 r \\
3 m & =14 r
\end{aligned}
$$

From this, we know that 3 divides $r$, hence $r \geqslant 3, m \geqslant 14$. Below is a construction of a performance schedule to show that $m=14$ is achievable:
$$
\begin{array}{l}
\{1,2,3,4\},\{5,6,7,8\},\{1,2,5,6\},\{3,4,7,8\},\{1,2,7,8\} \\
\{3,4,5,6\},\{1,3,5,7\},\{2,4,6,8\},\{1,3,6,8\},\{2,4,5,7\} \\
\{1,4,5,8\},\{2,3,6,7\},\{1,4,6,7\},\{2,3,5,8\}
\end{array}
$$

It is clear that the minimum number of performances that satisfy the conditions is 14.