PLATO was a network of systems, not just one. By 1978 there were PLATO systems in Illinois, Minnesota, Delaware, Florida, Belgium, and other locales, all internetworked using what was called "the link", a high-bandwidth connection between these various CYBER mainframes. PLATO had collectively many more users than ARPANET during this time; ARPANET's population wouldn't exceed PLATO's until probably around 1981, though it might even be later.

Here is Wikipedia page on PLATO: http://en.m.wikipedia.org/wiki/PLATO_(computer_system)