take a fano plane and apply all 5040 permutations of its 7 points. discard duplicate planes to obtain a set of 30 distinct fano planes. pick any of the 30, and pick the 14 others that have exactly one line in common with the first, not 0 or 3. the incidence structure between the 1+14 = 15 fano planes and the 35 triplets they mutually cover induces a pg(3,2).