Akitoshi Kawamura. Generalized semimagic squares for digital halftoning. Theory of Computing Systems 49(3), 632–638, October 2011. DOI = 10.1007/s00224-010-9290-7
Completing Aronov et al.'s study on zero-discrepancy matrices for digital halftoning, we determine all (m, n, k, l) for which it is possible to put mn consecutive integers on an m×n board (with wrap-around) so that each k×l region has the same sum. For one of the cases where this is impossible, we give a heuristic method to find a matrix with small discrepancy.