Is there an analogue of the [Beck-Fiala theorem](http://en.wikipedia.org/wiki/Beck%E2%80%93Fiala_theorem) for linear or hereditary discrepancies of hypergraphs?



Beck-Fiala for other discrepancies
If you take a subsystem, then the degree condition of the Beck-Fiala is still satisfied, so it is also trivially true for hereditary discrepancy. From Lovasz-Spencer-Vesztergombi, we know that the linear discrepancy can be bounded by twice the hereditary discrepancy, so almost the same bound applies for that as well.


