Abstract
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.
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References
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Kawamura, A. Generalized Semimagic Squares for Digital Halftoning. Theory Comput Syst 49, 632–638 (2011). https://doi.org/10.1007/s00224-010-9290-7
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DOI: https://doi.org/10.1007/s00224-010-9290-7