ZarankiewiczDB,

an online database of Zarankiewicz numbers.

z(22,22) = 108

Searching for matrices of weight greater than 108, all but 3 scaffolds were eliminated without search.

Scaffold: $p=4$, $q=4$, $\mathbf{m}=(4,4,4,4)$, $\mathbf{n}=(4,4,4,4)$, $m_O=1$, $n_O=1$.

(55.076250194 seconds, score = 0, 258562 recursive calls, max depth = 18)

Scaffold: $p=4$, $q=4$, $\mathbf{m}=(4,4,4,4)$, $\mathbf{n}=(4,4,4,3)$, $m_O=1$, $n_O=2$.

(0.004189638 seconds, score = 0, 0 recursive calls, max depth = 0)

Scaffold: $p=4$, $q=4$, $\mathbf{m}=(4,4,4,3)$, $\mathbf{n}=(4,4,4,3)$, $m_O=2$, $n_O=2$.

(0.001958349 seconds, score = 0, 0 recursive calls, max depth = 0)

upper bound = 108, submitted by Andrew Kay on April 23rd, 2016 (link)

By adding one row and one column to z(21,21), focused on an empty cell.

lower bound = 108, submitted on April 22nd, 2016 (link)

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