A subset A of a commutative semigroup X is called a B_h-set in X if the only solutions to a₁ + ··· + a_h = b₁ + ··· + b_h, a_i, b_i ∈ A are the trivial solutions {a₁,..., a_h} = {b₁,..., b_h} (as multisets). With h = 2 and X = Z, these sets are also known as Sidon sets, Golomb rulers, and Babcock sets. In this work, we generalize constructions of Bose-Chowla and Singer and give the resultant bounds on the diameter of a k element B_h-set in Z for h = 3, k ≤ 28 and h = 4, k ≤ 16. We conclude with a list of open problems.