Summary: Given $n$ strands of black and white pearls, each of length $k$. Assume that each pair of strands agree in at least $m$ more positions than they disagree, and that at each position the excess number of pearls of one color over the other across the strands is at most $d$. The authors find a necessary condition on $n,k,m$ and $d$, and prove it both combinatorially and by linear algebra.