Or encode the number using timing.
Further, you could send the bit as a pulse, where the pulse-width is proportional to the number.
Suppose you have two clocks that are synchronized to +-dt1, and sending messages takes some known amount of time +-dt2 and you want to make sure the sender is able to transmit within +dt3 of whatever event triggered the send event.
It seems to me that you'd be able to transmit at least dt3/(2*(dt1+dt2)) distinct values with the pretty naive approach of discretizing time into segments longer than the uncertainty between the message-and-clock error. I'd be willing to bet that a sophisticated approach could do much better.
It looks like PTP only works on a local network; not sure how you'd do that across the Internet.