Erdős Problem 734

### What is the conjecture

https://www.erdosproblems.com/734

Find, for all large $n$, a non-trivial pairwise balanced block design $A_1,\ldots,A_m\subseteq \\{1,\ldots,n\\}$ such that, for all $t$, there are $O(n^{1/2})$ many $i$ such that $\lvert A_i\rvert=t$.

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

The issue provides only the conjecture link and no repository file, test, or entry point. First inspect existing formalizations of Erdős problems in the Lean repository and the linked statement; done means adding a checked Lean formalization of Problem 734.

Written by the indexing model from the issue text.