  Atomic clocks occupy a unique position in measurement science, exhibiting
higher accuracy than any other measurement standard and underpinning six out of
seven base units in the SI system. By exploiting higher resonance frequencies,
optical atomic clocks now achieve greater stability and lower frequency
uncertainty than existing primary standards. Here, we report frequency ratios
of the $^{27}$Al$^+$, $^{171}$Yb and $^{87}$Sr optical clocks in Boulder,
Colorado, measured across an optical network spanned by both fiber and
free-space links. These ratios have been evaluated with measurement
uncertainties between $6\times10^{-18}$ and $8\times10^{-18}$, making them the
most accurate reported measurements of frequency ratios to date. This
represents a critical step towards redefinition of the SI second and future
applications such as relativistic geodesy and tests of fundamental physics.
