  It is known that Hall's sextic residue sequence has some desirable features
of pseudorandomness: an ideal two-level autocorrelation and linear complexity
of the order of magnitude of its period $p$. Here we study its correlation
measure of order $k$ and show that it is, up to a constant depending on $k$ and
some logarithmic factor, of order of magnitude $p^{1/2}$, which is close to the
expected value for a random sequence of length $p$. Moreover, we derive from
this bound a lower bound on the $N$th maximum order complexity of order of
magnitude $\log p$, which is the expected order of magnitude for a random
sequence of length $p$.
