  Drori and Teboulle [4] conjectured that the minimax optimal constant stepsize
for N steps of gradient descent is given by the stepsize that balances
performance on Huber and quadratic objective functions. This was numerically
supported by semidefinite program (SDP) solves of the associated performance
estimation problems up to $N\approx 100$. This note presents a strengthened
version of the initial conjecture. Specifically, we conjecture the existence of
a certificate for the convergence rate with a very specific low-rank structure.
This structure allows us to bypass SDPs and to numerically verify both
conjectures up to $N = 20160$.
