I added in those links, Neil. Thanks, Dan! Has anyone seen those orchard-planting polynomials before? Is there a way to generate them? It would be nice to hammer on the mirror symmetric and skew symmetric polynomials to see if any more sporadic solutions exist. I was really surprised when the simpler solution for sporadic 16 popped out at me. By the way -- the known sporadic 19 solution has absolutely nothing to do with zero-sum geometries. --Ed Pegg Jr