We provide an up-to-date view of the structure of the energy landscape of the
low autocorrelation binary sequences problem, a typical representative
of the $NP$-hard class. To study the landscape features of interest we use
the local optima network methodology through exhaustive extraction of the optima
graphs for problem sizes up to $24$. Several metrics are used to characterize the
networks: number and type of optima, optima basins structure, degree and strength distributions,
shortests paths to the global optima, and random walk-based centrality of optima.
Taken together, these metrics provide a quantitative and coherent explanation for
the difficulty of the low autocorrelation binary sequences problem
and provide information that could be exploited by optimization heuristics for this problem, as well as
for a number of other problems having a similar configuration space structure.