Relatively Narrow Latin Parallelepipeds That Cannot Be Extended to a Latin Cube

In this paper we construct a latin \((n \times n \times (n-d))\)-parallelepiped that cannot be extended to a latin cube of order \(n\) for any pair of integers \(d, n\) where \(d \geq 3\) and \(n \geq 2d+1\). For \(d = 2\), it is similar to the construction already known.