  The existence of a static lengthscale that grows in accordance with the
dramatic slowing down observed at the glass transition is a subject of intense
interest. A recent publication compared two proposals for this length scale,
one based on the point-to-set correlation technique and the other on the scale
where the lowest eigenvalue of the Hessian matrix becomes sensitive to
disorder. The conclusion was that both approaches lead to the same lengthscale,
but the former is easier to measure at higher temperatures and the latter at
lower temperatures. But even after using both methods together, the range of
increase in the observed lengthscales was limited by the relaxation times
reachable by standard molecular dynamics techniques (i.e. about 4-5 orders of
magnitude). In this paper we therefore attempt to explore the typical scale at
even lower temperatures, testing for this purpose two approaches, one based on
the idea of vapor deposition and the other on a swap Monte Carlo technique. We
conclude that the first approach does not help in getting to lower
temperatures, but the second one does so quite effectively. We can reach a
typical lengthscale that grows in accordance with at least $15$ orders of
magnitude increase in the relaxation time, competing with the best experimental
conditions. We conclude by discussing the relationship between the observed
lengthscale and various models of the relaxation time.
