How do I get past 28?

Look at the top of the door and you'll notice the green circles are in groups. Quickly input the number of taps each group is in going left to right. So you first need to double tap then wait for the door to go gray, then triple tap and wait for the screen to go gray, etc.

Pretty much exactly what SBF9034 said...
each dot carresponds to the number oftimes you have to tap it to get it to open.
you tap in twice, three times, once, and then twice again letting it turn gray between each group and then it will open.