Linear Hashing is Not That Awesome

Consider the canonical universal hash family $h(x)= ((ax+b)\text{ mod } p)\text{ mod } m$, where $a,b$ are chosen uniformly from $\mathbb Z_p$, which we call linear hashing, being used to hash $n$ elements into $m=Θ(n)$ buckets. For any universal family, the expected size of the largest bucket is at