a 3-(16,4,1) block design has 140 blocks of size 4 on 16 points, such that each triplet of points is covered exactly once. pick any single point, take only the 35 blocks containing that point, and delete that point. the 35 blocks of size 3 that remain comprise a pg(3,2) on the 15 remaining points. if these 16 points are arranged in a 4x4 grid and assigned 4-bit binary coordinates like in a karnaugh map for example, one gets the square representation. geometrically, the 35 lines are represented as a bijection with the 35 ways to partition a 4x4 grid into 4 regions of 4 cells each, if the grid represents an affine space and the regions are 4 parallel planes.