Asymptotic equivalence for nonlayerable arrays

Determine whether, for fixed d and n tending to infinity, the smallest k for which a nonlayerable (n^{d−1}, n−k)-array exists is asymptotically equal to NC_d(n).

Background

A nonlayerable array cannot be decomposed into layers, paralleling noncompletability of a Latin hypercuboid. This problem asks whether the threshold among all balanced set arrays agrees asymptotically with the completability threshold among realisable arrays.