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Problem 734 — Erdős Problems

Problem 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 $\lvert A_i\rvert=t$ .

Source: erdosproblems.com/734

Combinatorics

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Er81: Erdős, P., On the combinatorial problems which I would most like to see solved. Combinatorica (1981), 25-42.
dBEr48: de Bruijn, N. G. and Erdős, P., On a combinatorial problem. Nederl. Akad. Wetensch., Proc. (1948), 1277-1279 = Indagationes Math. 10, 421-423.

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Status: Open
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