Construction of infinite de Bruijn arrays (Q1114658)

We construct a periodic array containing every k-ary \(m\times n\) array as a subarray exactly once. Using the algorithm SUPER (which for \(k\geq 3\) generates an infinite k-ary sequence whose beginning parts of length \(k^ m\), \(m=1,2,...\), are de Bruijn sequences) we also construct infinite \(k^ m\times \infty\) k-ary arrays in which each beginning part of size \(k^ m\times k^{mn-m}\), \(n=1,2,...\), as a periodic array, contains every k-ary \(m\times n\) array exactly once.