I am pretty sure they recently tried a new method using quasars and found the expansion to be even faster, but I havent found any official values for this value.
Yeah, under the acronym "
H0LiCOW", where they measure the Hubble constant from gravitationally lensed images of quasars. The team has a nice short video explaining how the method works:
[youtube]qoVQ8f5nVOw[/youtube]
Combining the measurements of 4 such lensed quasars leads them to a value of 72.5km/s/Mpc, plus or minus about 2.2:
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[left]The strength of this method is that it doesn't depend on the cosmic distance ladder, where we chain together several different methodologies of measuring distances, from short scales to longer. In that sense this is a very independent form of measurement of the expansion rate. The downside is that it does rely on knowledge of the geometry of the lens, and the amount of matter in the universe. So to make the error bars as small as they claim, they need to combine their data with measurements of the matter density and curvature of the universe from Planck data.[/left]
[left]This value is also only based on 4 objects, so the precision may continue to improve as more of these multiply-imaged quasars are discovered and studied.

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[left]Another independent measurement of the Hubble constant can be done from gravitational wave events, if the event is connected to a visible source, as was the case with the binary neutron star merger a couple years ago. The gravitational waves tell us how far away the event occurred, and the electromagnetic observations tell us how much it was redshifted, so together this acts as a measurement of the expansion rate. Unfortunately, with one event and large uncertainties on its distance, the error bars are huge and don't tell us "who is right" about the Hubble constant. But again with more of these events detected in the future, they very well could help pin it down.[/left]