  In this work, a classical problem of the digital sequence design, or more
precisely, finding binary sequences with optimal peak sidelobe level (PSL), is
revisited. By combining some of our previous works, together with some
mathematical insights, few hybrid heuristic algorithms were created. During our
experiments, and by using the aforementioned algorithms, we were able to find
PSL-optimal binary sequences for all those lengths, which were previously found
during exhaustive searches by various papers throughout the literature. Then,
by using a general-purpose computer, we further demonstrate the effectiveness
of the proposed algorithms by revealing binary sequences with lengths between
106 and 300, the majority of which possess record-breaking PSL values. Then, by
using some well-known algebraic constructions, we outline few strategies for
finding highly competitive binary sequences, which could be efficiently
optimized, in terms of PSL, by the proposed algorithms.
