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

**Full text on arXiv**(September 7, 2010)

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.