Exact maximum size of Sidon sets in F_2^n

Determine the exact maximum possible cardinality of a Sidon set in F_2^n for dimensions n≥10.

Background

A major extremal problem motivating the paper is to determine the largest possible size of a Sidon set in the vector space F_2n. The paper notes that the exact answer is known only for n≤10 in the cited literature, while its later construction improves lower bounds in selected dimensions.

The unresolved status concerns the exact extremal value, not merely the construction of large examples; the paper explicitly states that the maximum remains unknown for n≥10.

References

Despite many different constructions, finding the exact maximum size of a Sidon set in F_2n is still unknown for n \geq 10.

— On generalizing cryptographic results to Sidon sets in $\mathbb{F}_2^n$  (2501.11184 - Thornburgh, 19 Jan 2025) in Section 2, subsection “Background on Sidon sets”; reiterated in Section 5