Construction of infinite de Bruijn arrays

Abstract We construct a periodic array containing every k-ary m × n array as a subarray exactly once. Using the algorithm SUPER (which for k⩾3 generates an infinite k-ary sequence whose beginning parts of length km, m = 1,2,..., are de Bruijn sequences) we also construct infinite km × ∞ k-ary arrays in which each beginning part of size km × kmn − m, n = 1,2,..., as a periodic array, contains every k-ary m × n array exactly once.