Consider the set ( F 3) 6 of all 6 tuples x=( x 1,…, x 6) with x i ϵ {0, 1, 2}. We show that there exists a subset T of ( F 3) 6 with 79 elements such that for any x of ( F 3) 6 there is an element if T which differs from x in at most one coordinate.