  Double neutron star (DNS) systems are produced from massive binaries. A
supernova (SN) explosion of an extremely stripped star is expected to occur at
the final stage of DNS formation. This type of SN is called ultra-stripped SN
(USSN). A recent research reveals that a type Ic SN, iPTF 14gqr (SN 2014ft) has
low ejecta mass ($\approx0.2~\mathrm{M}_\odot$) and its progenitor has a helium
envelope with its mass $\sim0.01~\mathrm{M}_\odot$. Then this SN is interpreted
as an USSN, and this is the first discovery of the USSN. Furthermore, the
observation of iPTF 14gqr provides us with some information about its formation
history. Here, we perform population synthesis calculations so as to estimate
the detection rate of iPTF 14gqr like USSNe by optical transient surveys,
intermediate Palomar Transient Factory (iPTF), Zwicky Transient Facility (ZTF),
and Large Synoptic Survey Telescope (LSST). We find that iPTF, ZTF, and LSST
can observe iPTF 14gqr like USSNe at the rates of 1, 40, and 5
$\mathrm{yr}^{-1}$, respectively. The iPTF may detect 4 iPTF 14gqr like USSNe
during four years observation. Additionally, we investigate effects of some
binary physics on the orbital parameters of DNS systems and formation channels.
