  A $k$-permutation family on $n$ vertices is a set system consisting of the
intervals of $k$ permutations of the integers $1$ through $n$. The discrepancy
of a set system is the minimum over all red-blue vertex colorings of the
maximum difference between the number of red and blue vertices in any set in
the system. In 2011, Newman and Nikolov disproved a conjecture of Beck that the
discrepancy of any $3$-permutation family is at most a constant independent of
$n$. Here we give a simpler proof that Newman and Nikolov's sequence of
$3$-permutation families has discrepancy $\Omega(\log n)$. We also exhibit a
sequence of $6$-permutation families with root-mean-squared discrepancy
$\Omega(\sqrt{\log n})$; that is, in any red-blue vertex coloring, the square
root of the expected difference between the number of red and blue vertices in
an interval of the system is $\Omega(\sqrt{\log n})$.
