Polycross designs with complete neighbor balance

Summary

Polycross designs for n clones in n² replicates, composed of n n×n squares, are presented, n being any positive integer. The method depends on whether n is odd or even, and for even n the squares are Latin. In either case, each clone has every other clone as a nearest neighbor exactly n times in each of the four primary directions (N, S, E, W) and n−2 times in each of the four intermediate directions (NE, SE, SW, NW). Also, each clone has itself as nearest neighbor n−1 times in each intermediate direction.