Aperiodic autocorrelation of Frank sequences

It is well known that Frank sequences are a class of polyphase sequences with ideal periodic autocorrelation functions. It is shown that some of the Frank sequences also have very favourable aperiodic autocorrelations. For Frank sequences of length L=q², there exist two sequences whose maximum out-of-phase aperiodic autocorrelation values are asymptotic to q/π as q tends to infinity. If L is odd, there exist two sequences whose maximum out-of-phase aperiodic autocorrelation values are bounded by 2√((2)(q/π))