Generalized Semimagic Squares for Digital Halftoning

摘要

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.