In 2021, Balogh-Füredi-Roy proved that any Sidon set with $k$ elements has diameter at least $k^2 − 1.996k^{3/2}$, provided that $k$ is sufficiently large. We give a method logically simpler than the BFR one, though trading on the same phenomena, but substantively more involved computationally. The diameter of a $k$ element Sidon set is at least $k^2 − 1.99405k^{3/2}$.
Kevin O'Bryant