Derandomize MAX-CUT problem using $\log n$ bits
Consider a graph with $n$ vertices and $m$ edges.

Let $\mathcal{D}$ be a pairwise independent distribution over $\{0,1\}^n$, and suppose that $x = (x_1,\ldots,x_n) \sim \mathcal{D}$. For every edge $(i,j)$, the probability that it is cut in the cut corresponding to $x$ is
$$
\Pr[x_i \neq x_j] = \frac{1}{2},
$$
due to pairwise independence. Therefore the expected number of edges cut is exactly $\frac{m}{2}$, by linearity of expectation. In particular, there is at least one realization of $x$ (that is, one point in the support of $\mathcal{D}$) which cuts at least $m/2$ edges.