  Fast Radio Bursts (FRBs), are millisecond radio signals that exhibit
dispersion larger than what the Galactic electron density can account for. We
have conducted a 1446 hour survey for Fast Radio Bursts (FRBs) at 145~MHz,
covering a total of 4193 sq. deg on the sky. We used the UK station of the
LOFAR radio telescope -- the Rawlings Array -- , accompanied for a majority of
the time by the LOFAR station at Nan\c{c}ay, observing the same fields at the
same frequency. Our real-time search backend, ARTEMIS, utilizes graphics
processing units to search for pulses with dispersion measures up to 320
cm$^{-3}$ pc. Previous derived FRB rates from surveys around 1.4~GHz, and
favoured FRB interpretations, motivated this survey, despite all previous
detections occurring at higher dispersion measures. We detected no new FRBs
above a signal-to-noise threshold of 10, leading to the most stringent upper
limit yet on the FRB event rate at these frequencies: 29 sky$^{-1}$ day$^{-1}$
for 5~ms-duration pulses above 62~Jy. The non-detection could be due to
scatter-broadening, limitations on the volume and time searched, or the shape
of FRB flux density spectra. Assuming the latter and that FRBs are standard
candles, the non-detection is compatible with the published FRB sky rate, if
their spectra follow a power law with frequency ($\propto \nu^{\alpha}$), with
$\alpha\gtrsim+0.1$, demonstrating a marked difference from pulsar spectra. Our
results suggest that surveys at higher frequencies, including the low frequency
component of the Square Kilometre Array, will have better chances to detect,
estimate rates and understand the origin and properties of FRBs.
