band. We have also placed improved upper limits on the existence of a  from vector and scalar-polarized gravitational waves.

While the upper limits on the SGWB presented in this work are the strongest direct limits in the frequency band of current ground-based gravitational-wave detectors, other observations place stronger constraints in other frequency bands. The NANOGrav collaboration has reported the 95% upper limit of $\Omega_{\rm GW} < 7.4\times 10^{-10}$ at a frequency of $1\ {\rm yr}^{-1}$ after marginalizing over uncertainty in the solar system ephemeris [@Arzoumanian:2018saf]. Combining data from the *Planck* satellite and the BICEP2/Keck array constrain the tensor-to-scalar ratio from the CMB to be $r<0.064$ at 95% confidence at comoving scales of $k=0.002\ {\rm Mpc^{-1}}$, corresponding to a gravitational wave frequency of $f_{0.002}=(2\pi)^{-1} ck=3.1\times 10^{-18} {\rm Hz}$ [@Akrami:2018odb], assuming the single field slow roll consistency condition. Using Equation 4 of [@Lasky:2015lej], this can be converted into the constraint $\Omega_{\rm GW}(f)\leq 3.2 \times 10^{-16} \times (f/f_{\rm 0.05})^{-r/8}\left[16/9+f_{\rm eq}^{2}/(2f^2)\right]$, where $f_{\rm eq}$ is the frequency of a gravitational wave of which the wavelength was the size of the Universe at matter-radiation equality, and $f_{\rm 0.05}$ is the pivot scale. Combining constraints at different frequency ranges can probe models which span many orders 