  We evaluate the potential for gravitational-wave (GW) detection in the
frequency band from 10 nHz to 1 $\mu$Hz using extremely high-precision
astrometry of a small number of stars. In particular, we argue that
non-magnetic, photometrically stable hot white dwarfs (WD) located at $\sim$
kpc distances may be optimal targets for this approach. Previous studies of
astrometric GW detection have focused on the potential for less precise surveys
of large numbers of stars; our work provides an alternative optimization
approach to this problem. Interesting GW sources in this band are expected at
characteristic strains around $h_c \sim 10^{-17} \times
\left(\mu\text{Hz}/f_{\text{GW}}\right)$. The astrometric angular precision
required to see these sources is $\Delta \theta \sim h_c$ after integrating for
a time $T \sim 1/f_{\text{GW}}$. We show that jitter in the photometric center
of WD of this type due to starspots is bounded to be small enough to permit
this high-precision, small-$N$ approach. We discuss possible noise arising from
stellar reflex motion induced by orbiting objects and show how it can be
mitigated. The only plausible technology able to achieve the requisite
astrometric precision is a space-based stellar interferometer. Such a future
mission with few-meter-scale collecting dishes and baselines of
$\mathcal{O}(100\text{ km})$ is sufficient to achieve the target precision.
This collector size is broadly in line with the collectors proposed for some
formation-flown, space-based astrometer or optical synthetic-aperture
imaging-array concepts proposed for other science reasons. The proposed
baseline is however somewhat larger than the km-scale baselines discussed for
those concepts, but we see no fundamental technical obstacle to utilizing such
baselines. A mission of this type thus also holds the promise of being one of
the few ways to access interesting GW sources in this band.
