Asymptotic equivalence for arrays containing no layer

Determine whether, for fixed d and n tending to infinity, the smallest k for which an (n^{d−1}, n−k)-array contains no layer is asymptotically equal to NE_d(n).

Background

Unused-symbol arrays arising from Latin hypercuboids are realisable arrays, but not every balanced set array is necessarily realisable. The question asks whether ignoring realisability changes the asymptotic threshold for the existence of an array with no single layer.