Block designs

In this paper, we assume a proper pairwise balanced design on 30 points exists. We then get some results that reveal what the largest line size may be and the maximum number of lines of this size. Using these results, we look at one of two cases. We investigate the structure of the linear spaces in this case having no lines of sizes 2, 3, 6 and 30 and rule out many possibilities in order to get a minimum number of possible solutions.