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

A note on Hall's sextic residue sequence: correlation measure of order $k$ and related measures of pseudorandomness