# ZarankiewiczDB,

an online database of Zarankiewicz numbers.

## z(15,26) = 86

Searching for matrices of weight greater than 86, all but 6 scaffolds were eliminated without search.

Scaffold: $p=3$, $q=5$, $\mathbf{m}=(5,5,4)$, $\mathbf{n}=(2,2,2,2,2)$, $m_O=6$, $n_O=1$.

(5.723503649 seconds, score = 0, 56347 recursive calls, max depth = 29)

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

(0.00118004 seconds, score = 0, 0 recursive calls, max depth = 0)

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

(2139.882428159 seconds, score = 0, 17392608 recursive calls, max depth = 33)

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

(23625.131643493 seconds, score = 0, 198715169 recursive calls, max depth = 40)

Scaffold: $p=3$, $q=5$, $\mathbf{m}=(5,5,4)$, $\mathbf{n}=(3,2,2,2,2)$, $m_O=6$, $n_O=0$.

(56615.385421823 seconds, score = 0, 488154622 recursive calls, max depth = 36)

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

(100547.639108755 seconds, score = 0, 852073626 recursive calls, max depth = 38)

upper bound = 86, submitted by Andrew Kay on April 28th, 2016 (link)

By adding a column of weight 1 to z(15,25).

lower bound = 86, submitted on April 28th, 2016 (link)

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