# 3x3 submatrix with only $0$ or $1$ entries

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.

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According to this: MR1622032 (99c:05139) Hattingh, Johannes H.(SA-RAND); Henning, Michael A.(SA-NTL2) Bipartite Ramsey theory. (English summary) Util. Math. 53 (1998), 217–230. the answer is $17$, not $15.$