On the Size of Finite Sidon Sets

Sidon set (also called a Golomb ruler) is a B₂ sequence and a 1-thin set is a set of integers containing no nontrivial solutions to the equation a + b = c + d. We improve the lower bound for the diameter of a Sidon set with k elements, namely, if k is sufficiently large and \(\mathcal{A}\) $\mathcal{A}$ is a Sidon set with k elements, then diam( \(\mathcal{A}\) $\mathcal{A}$ ) ≥ k² −1.99405k^3/2. Alternatively, if n is sufficiently large, then the cardinality of the largest subset of {1, 2, . . . ,n}, which is a Sidon set, does not exceed n^1/2 + 0.99703n^1/4.