Lower-order correction for finite-field Kakeya sets

Determine the lower-order correction to the leading asymptotic term for the minimum size of finite-field Kakeya sets, beyond the settled leading constant.

Background

The paper explains that Bukh and Chao settled the leading asymptotic constant for finite-field Kakeya sets in every fixed dimension, including the value 1/4 in dimension 3. The unresolved issue is the lower-order behavior, particularly the coefficients of terms below the leading pd scale.

The paper’s new infinite family improves known finite and lower-order bounds in dimension three, but it does not determine the optimal lower-order correction.

References

What remains open is the lower-order correction to this leading term.

— Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment  (2608.23691 - Chung et al., 24 Aug 2026) in Section 3, subsection “Finite-field Kakeya”