  The Baryon Acoustic Oscillations (BAO) refer to the ripples of material
density in the Universe. As the most direct density tracers in the universe,
galaxies have been commonly used in studies of BAO peak detection. The spatial
number density of galaxies, to a certain extent, reflects the distribution of
the material density of our Universe. Using galaxies as matter tracers, we can
construct more overlapping empty spheres (DT voids) than the matter tracers,
via Delaunay Triangulation technique. We show that their radii excellently
reflect the galaxy number density round them, and they can serve as reliable
different density region tracers. Using the data from an unprecedented
large-scale $N$-body simulation "TianNu", we conduct some fundamental
statistical studies and clustering analysis of the DT voids. We discuss in
detail the representative features of two-point correlation functions of
different DT void populations. We show that the peak, the position of which
corresponds to the average radius of data samples, is the most representative
feature of the two-point correlation function of the DT voids. In addition, we
also construct another voids, the disjoint voids, and investigate their some
statistical properties and clustering properties. And we find that the occupied
space of all disjoint voids accounts for about $45\%$ of the volume of the
simulation box, regardless of the number density of mock galaxies. We also
investigate the BAO detections based on different tracers, i.e. mock galaxies,
low-density region tracers, and high-density region tracers respectively. Our
results show that BAO intensities detected by low/high-density region tracers
are enhanced significantly compared to the BAO detection by mock galaxies, for
the mock galaxy catalogue with the number density of $7.52\times10^{-5}$ $h^3$
Mpc$^{-3}$.
