I decided to cross-post the question here from math.stackexchange.com because I got no answer from there.

It is a quick question on bipartite Ramsey numbers (I'm not an expert on the subject, so perhaps the question is trivial).

What is the least positive integer $r$ such that, any $r \times r$ 0-1 matrix contains at least one $3 \times 3$ submatrix filled with only 0 or only 1 entries ?

I found some articles with upper/lower bounds, but not a clear chart with the particular values I need.