The problem I have is the visualisation of a 1-(50,15,15) design. That is a set of 50 points and 50 blocks (lines), so that each point is on 15 lines, and each line contains 15 points.
My attempts thus far have been on Mathematica. I have managed to create a graph with 50 points and 750 edges, so obviously the problem is putting 15 points on a given edge.
A graph by definition has only two vertices on each edge, so I don't think you can use the "graph" object in Mathematica to model this (at least not in this way).
You can do a bipartite graph with one part corresponding to the points and another to the blocks. So you will have 100 vertices total, and the graph will be $15$-regular.