I think some of people complaining about buzz and noise are experiencing a ground loop with PC/ntb. Fortunately TPA3116 offers balanced inputs which allow for complete elimination of the ground loop effects. It worked in my case Adding an Amp into Thin-Client PC
Thanks Dave, I'm still battling with a buzz that's evident at higher volume. I'll certainly try the battery option - I have a few 12V 7Ah batteries available for testing.
I'm using a fairly recent HP Pavilion laptop as the source, I assume it's grounded but I could be wrong.
The power supply for the amp is not grounded and I haven't checked where to connect ground - it's one of these:
AC Converter 110v 220v to 12V MAX 8A 100W Regulated Transformer LED Power Supply | eBay
Any specific reason why you're only using 12v? Most available boards can take 24v safely, with some considering 19v the sweetspot.
My error - I'm actually using the 24V version that looks pretty much identical.
I use a 24v version on some of my 3116's as well, hence my original question...
That combination should not produce a standard ground loop as the amp is not grounded. Still the Y-capacitor in the 24V PSU does leak quite a bit of noise. I can see it on my measurement results when my class-I scope is hooked to a class-II measurement computer - no "real" ground loop, yet the measurement gets way worse.
Even in this case I would try the SE-balanced connection. It may work surprises.
I recently bought 2.1 channel TPA3116D2 board, almost like this one:
New 2x50W +100W 2.1 Channel Digital Subwoofer Power Amplifier Board TPA3116D2 699903978280 | eBay
And it has a lot of buzz and hiss with any switching power supply, and if I connect it to old style transformer power supply, it all was gone, but since transformer was no go for me, I tried a lot of things, and finally found a solution - soldered 1uf ceramic capacitor with short leads directly to 4 and 8 pins of rightmost IC in 8 pin case (as shown on ebay listing picture). All buzz and hiss had gone now!
New 2x50W +100W 2.1 Channel Digital Subwoofer Power Amplifier Board TPA3116D2 699903978280 | eBay
And it has a lot of buzz and hiss with any switching power supply, and if I connect it to old style transformer power supply, it all was gone, but since transformer was no go for me, I tried a lot of things, and finally found a solution - soldered 1uf ceramic capacitor with short leads directly to 4 and 8 pins of rightmost IC in 8 pin case (as shown on ebay listing picture). All buzz and hiss had gone now!
CuriousOne, I agree that a radical way to reduce noise of class D + PowerSupply is a 60Hz trafo+diodes but not any SMPS so crappy as you expect yet. I have TPA3116 based 2-way(bi-amping) studio monitor project, with DSP ADAU1701 as a preamp, which has S/N = -104db(A) at tweeter output. The SMPS onboard is almost trivial quasi-resonant flyback with spike recuperation. I don't believe if 60Hz trafo, instead that SMPS, may improve S/N for single one db 
12Vac/200VA will be more than enough. You can also go up to 15Vac/200VA and get more output power.
I have access to a couple of the 12/200 and I fancy building a linear psu!
(35V-24V)*5A=55W of power wasted on linear regulator. Why you should do that?
For the power supplies for amplifiers, I usually hunt for transformers from old UPS-es. In general, they have two secondary windings with 7.5V AC and 5-15A current. Connect them in series and you will get 15VAC, which is about 20VDC and is great for most class D amps. If you can get UPS which used 24V battery, it will have 2x15VAC windings, which means you can use more powerful Class D amplifiers, which require +-20V and more voltage to operate.
For the power supplies for amplifiers, I usually hunt for transformers from old UPS-es. In general, they have two secondary windings with 7.5V AC and 5-15A current. Connect them in series and you will get 15VAC, which is about 20VDC and is great for most class D amps. If you can get UPS which used 24V battery, it will have 2x15VAC windings, which means you can use more powerful Class D amplifiers, which require +-20V and more voltage to operate.