A new construction of two-dimensional arrays with the window property

It is shown how row-complete Latin squares and Tuscan squares can be used to construct nonbinary 1-D and 2-D arrays that have the u ×v horizontal and/or vertical window property for all sufficiently large windows. It is shown how binary arrays with a similar property can be derived. Since an array can only be a perfect map for one particular size of window, the arrays that are constructed are not perfect but nevertheless have several practical applications, among others in connection with the coding and transmission of pictures. The method is deterministic rather than stochastic, and the arrays derived contain an effectively random selection of the windows of each relevant size