  We present the spectroscopic discovery of 69 quasars at 5.8 < z < 7.0, drawn
from the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) imaging survey
data. This is the 16th publication from the Subaru High-z Exploration of
Low-Luminosity Quasars (SHELLQs) project, and completes identification of all
but the faintest candidates (i.e., i-band dropouts with zAB < 24 and y-band
detections, and z-band dropouts with yAB < 24) with Bayesian quasar probability
Pq > 0.1 in the HSC-SSP third public data release (PDR3). The sample reported
here also includes three quasars with Pq < 0.1 at z ~ 6.6, which we selected in
an effort to completely cover the reddest point sources with simple color cuts.
The number of high-z quasars discovered in SHELLQs has now grown to 162,
including 23 type-II quasar candidates. This paper also presents identification
of seven galaxies at 5.6 < z < 6.7, an [O III] emitter at z = 0.954, and 31
Galactic cool stars and brown dwarfs. High-z quasars and galaxies comprise 75 %
and 16 % respectively of all the spectroscopic SHELLQs objects that pass our
latest selection algorithm with the PDR3 photometry. That is, a total of 91 %
of the objects lie at z > 5.6. This demonstrates that the algorithm has very
high efficiency, even though we are probing an unprecedentedly low-luminosity
population down to M1450 ~ -21 mag.
