i2s over HDMI is not an industry standard. There are several vendors that use HDMI cable to transfer i2s, but that doesn't mean that any transport can be connected to any DAC using HDMI/i2s.
For example, both Wyred4Sound and PS Audio have solutions that transfer i2s over an HDMI cable. However, the pin configurations are completely different, which means that you cannot just connect a PS Audio transport to a Wyred4Sound DAC using i2 over HDMI.
Some companies also transfer i2s over an RJ45 cable (same as ethernet). Their pin configurations may be different as well.
If you're really interested, I would check with the vendors on those products and ask them about their i2s/HDMI pin configurations to see if they are compatible.
You can always upgrade to different digital COAX cables and that will have a significant improvement as well.
For example, both Wyred4Sound and PS Audio have solutions that transfer i2s over an HDMI cable. However, the pin configurations are completely different, which means that you cannot just connect a PS Audio transport to a Wyred4Sound DAC using i2 over HDMI.
Some companies also transfer i2s over an RJ45 cable (same as ethernet). Their pin configurations may be different as well.
If you're really interested, I would check with the vendors on those products and ask them about their i2s/HDMI pin configurations to see if they are compatible.
You can always upgrade to different digital COAX cables and that will have a significant improvement as well.