  The present work aims to build a new statistical distance scale for planetary
nebulae (PNe) based on a rigorous calibration sample. The distances of the
calibration sample are derived from the trigonometric parallax method using the
recent measurements of Gaia early third data release (Gaia EDR3). The new
distance scale is created by applying the well-known linear relationship
between the radio surface brightness temperature and the nebular radius. The
calibration sample is made up of 96 PNe of accurately computed distances with
uncertainties less than $20\%$. Earlier ground- and space-based trigonometric
parallaxes of PNe display inconsistency with those of Gaia, particularly the
HIPPARCOS results. In addition, these measurements have appreciably lower
precision than that of Gaia. When compared to the trigonometric technique, the
expansion and kinematic methods exhibited more consistency than the
spectroscopic, extinction, gravity, and photo-ionization methods. Furthermore,
contrary to earlier results in the literature, the extinction and gravity
methods, on average, underestimate and slightly overestimate the PN distances.
As a byproduct of extracting the Gaia parallaxes, we detect the radial velocity
and variability for 14 and 3 PN central stars (CSs), respectively. To our
knowledge, the variability of Hen 2-447 CS has been determined for the first
time.
