  A primordial black hole (PBH) with mass $10^{-15}\leq M_{\rm
PBH}/M_{\odot}\leq 10^{-10}$ is currently beyond the sensitivity of both
microlensing and black hole (BH) evaporation methods. A novel scenario has been
proposed: When a PBH with mass $10^{-14}\leq M_{\rm PBH}/M_{\odot}\leq
10^{-11}$ transits through a white dwarf (WD) made up of carbon and oxygen,
Bondi-Hoyle-Lyttleton (BHL) accretion in a reactive medium creates a shock
wave, which generates direct detonation ignition in the WD core and then leads
to thermonuclear supernovae (SNe Ia). The aim of this study is to impose
constraints on the PBH to dark matter (DM) abundance fraction, $f_{\rm PBH}$,
via comparing the SN Ia event rates between PBH hypotheses and observational
data. For PBH fraction less than unity, we found the observed event rate
prefers PBH mass region, $7.6\times 10^{-13}\leq M_{\rm PBH}/M_{\odot}\leq
6.1\times 10^{-12}$, under the Navarro-Frenk-White (NFW) profile. Meanwhile,
the aforementioned PBH mass and abundance can be efficiently produced via a
cosmological first-order phase transition (FOPT) in dark sector which
associates with $\mathcal{O}({\rm MeV})$ energy scale and thus gives rise to
complementary signals of stochastic gravitational waves (GWs) from $10^{-6}$ Hz
to $10^{-5}$ Hz peak frequency which can be probed by future $\mu$Ares GW
interferometer.
