BIGGER AND BETTER SUBSET-SUM-DISTINCT SETS

Call a set of natural numbers subset-sum-distinct (or SSD) if all pair wise distinct subsets have unequal sums. One wants to construct SSD se ts in which the largest element is as small as possible. Given any SSD set, it is easy to construct an SSD set with one more element in whic h the biggest element is exactly double the biggest element in the ori ginal set. For any SSD set, we construct another SSD set with k more e lements whose largest element is less than 2(k) times the largest elem ent in the original set. This claim has been made previously for a dif ferent construction, but we show that that claim is false.