Improving upon 2010 results of Alon  et al. , it was shown in 2014 by Schmidt that asymptotically, almost all binary sequences of length    $n$    have peak sidelobe level close to    $({2n\log n})^{1/2}\vphantom {\sum ^{R^{R}}}$   . One specific result of Alon  et al.  is that if we fix    $ \varepsilon >0$   , then almost all binary sequences of length    $n$    have peak sidelobe level at most    $({2n(\log n-(1.5- \varepsilon )\log \log n)})^{1/2}$   , in the sense that the probability of not satisfying that bound approaches 0 as    $n$    approaches infinity. In this note, we prove that for all sequence lengths    $n>1$   , there is a binary sequence of length    $n$    with peak sidelobe level at most    $({2n(\log n-\log \log n+0.862)})^{1/2}$   .
['Idris Mercer']
Bounding the Peak Sidelobe Level of Binary Sequences of All Lengths