# ZarankiewiczDB,

an online database of Zarankiewicz numbers.

## z(15,27) = 88

Searching for matrices of weight greater than 88, all but 4 scaffolds were eliminated without search.

Scaffold: $p=3$, $q=5$, $\mathbf{m}=(5,5,4)$, $\mathbf{n}=(2,2,2,2,2)$, $m_O=7$, $n_O=1$.

(507.927297033 seconds, score = 0, 4516253 recursive calls, max depth = 37)

Scaffold: $p=3$, $q=5$, $\mathbf{m}=(5,5,5)$, $\mathbf{n}=(2,2,2,2,2)$, $m_O=6$, $n_O=1$.

(8.80225E-4 seconds, score = 0, 0 recursive calls, max depth = 0)

Scaffold: $p=3$, $q=5$, $\mathbf{m}=(5,5,4)$, $\mathbf{n}=(3,2,2,2,2)$, $m_O=7$, $n_O=0$.

(318717.971949801 seconds, score = 0, 2675983769 recursive calls, max depth = 38)

Scaffold: $p=3$, $q=5$, $\mathbf{m}=(5,5,5)$, $\mathbf{n}=(3,2,2,2,2)$, $m_O=6$, $n_O=0$.

(39381.677618308 seconds, score = 0, 330494390 recursive calls, max depth = 36)

upper bound = 88, submitted by Andrew Kay on May 3rd, 2016 (link)

By deleting 16 rows and 4 columns from the finite projective plane of order 5.

lower bound = 88, submitted on May 3rd, 2016 (link)

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