That is actually not related, but the beginning of an entirely different field of mathematics. Design theory is the study of mathematical objects called combinatorial designs[1], which are basically fancy ways of partitioning finite sets into subsets with a pre-specified structure. The thing you linked to is a specific instance that shows the existence of designs in a few specific cases.

While Kirkman essentially posed the first design theory question in the 1850's, both the authors of one of the standard textbooks[2] in the field are still alive and (IIRC) still working today!

[1] https://en.wikipedia.org/wiki/Combinatorial_design . Incidentally, the field is called "design theory," but it's not a great search term outside of MathSciNet.

[2] http://www.amazon.com/Design-Edition-Discrete-Mathematics-Ap...