  The time-symmetric block time--step (TSBTS) algorithm is a newly developed
efficient scheme for $N$--body integrations. It is constructed on an era-based
iteration. In this work, we re-designed the TSBTS integration scheme with
dynamically changing era size. A number of numerical tests were performed to
show the importance of choosing the size of the era, especially for long time
integrations. Our second aim was to show that the TSBTS scheme is as suitable
as previously known schemes for developing parallel $N$--body codes. In this
work, we relied on a parallel scheme using the copy algorithm for the
time-symmetric scheme. We implemented a hybrid of data and task parallelization
for force calculation to handle load balancing problems that can appear in
practice. Using the Plummer model initial conditions for different numbers of
particles, we obtained the expected efficiency and speedup for a small number
of particles. Although parallelization of the direct $N$--body codes is
negatively affected by the communication/calculation ratios, we obtained good
load balance results. Moreover, we were able to conserve the advantages of the
algorithm (e.g., energy conservation for long--term simulations).
