Completing Aronov et al.'s study on zero-discrepancy matrices for digitalhalftoning, we determine all (m, n, k, l) for which it is possible to put mnconsecutive integers on an m-by-n board (with wrap-around) so that each k-by-lregion holds the same sum. For one of the cases where this is impossible, wegive a heuristic method to find a matrix with small discrepancy.
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