Discrepancy in different numbers of colors

In this article, we investigate the interrelation between the discrepancies of a given hypergraph in different numbers of colors. Being an extreme example we determine the multi-color discrepancies of the J._balanced hypergraph jf; on partition classes of (equal) size H. Let c,k,n£M. Set ko := k mode and b,kc'.= (n -[n/lc/k]\)k/c. For the discrepancy in c colors we show Z>,AOC < disc(jfA,c) < bhc + l, if ä-O/O, and disc(3f k-, c) = 0, if c divides k. This shows that, in general, there is little correlation between the discrepancies of Jft in different numbers of colors. If c divides k though, disc(Jf,c) < (k/c)disc(H,A-) holds for any hypergraph Jf.