ZarankiewiczDB,

an online database of Zarankiewicz numbers.

Recent submissions

Matrix for z(16,30)

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Found by the scaffold algorithm.

weight = 100, submitted by Andrew Kay on July 12th, 2017 (link, raw)

Matrix for z(15,30)

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Found by the scaffold algorithm.

weight = 95, submitted by Andrew Kay on June 30th, 2017 (link, raw)

Matrix for z(14,30)

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Found by the scaffold algorithm.

weight = 89, submitted by Andrew Kay on June 30th, 2017 (link, raw)

Bound for z(26,31)

Using the scaffold algorithm, all scaffolds were eliminated without search

upper bound = 156, submitted by Andrew Kay on June 30th, 2017 (link)

Bound for z(25,31)

Using the scaffold algorithm, all scaffolds were eliminated without search.

upper bound = 151, submitted by Andrew Kay on June 30th, 2017 (link)

Bound for z(21,30)

By the scaffold algorithm.

upper bound = 126, submitted by Andrew Kay on June 30th, 2017 (link)

Bound for z(20,30)

Using the scaffold algorithm.

upper bound = 121, submitted by Andrew Kay on June 28th, 2017 (link)

Bound for z(18,29)

By the Scaffold algorithm (all but 5 scaffolds eliminated without search).

upper bound = 108, submitted by Andrew Kay on May 24th, 2017 (link)

Matrix for z(9,7 | 1,2)

 1 1 1 2 2 2 1 2 1 2 1 2 1 2 2 1 1 2 1 2 1 2 2 1 1 1 2 1 2 1 1 1 2 2 1 1 2 2 1

Found by the quotient matrix algorithm. $i$ indicates an X in subrow $i$.

(57.144461372 seconds, score = 39, 1401477 recursive calls, max depth = 39)

weight = 39, submitted by Andrew Kay on July 28th, 2016 (link, raw)

Matrix for z(16,29)

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Found by the scaffold algorithm.

(479.030484105 seconds, score = 98, 9672735 recursive calls, max depth = 42)

lower bound = 98, submitted by Andrew Kay on July 28th, 2016 (link, raw)

Bound for z(14,29)

By adding a column of weight 1 to z(14,28).

lower bound = 87, submitted on July 26th, 2016 (link)

Bound for z(14,29)

Searching for matrices of weight greater than 87, all but 2 scaffolds were eliminated without search.

Scaffold: $p = 6$, $q = 2$, $\mathbf{m} = (2,2,2,2,2,1)$, $\mathbf{n} = (6,6)$, $m_O = 0$, $n_O = 10$.

(111.32385244 seconds, score = 0, 1874616 recursive calls, max depth = 44)

Scaffold: $p = 6$, $q = 2$, $\mathbf{m} = (2,2,2,2,2,1)$, $\mathbf{n} = (6,5)$, $m_O = 0$, $n_O = 11$.

(992.055214053 seconds, score = 0, 17033070 recursive calls, max depth = 46)

upper bound = 87, submitted by Andrew Kay on July 26th, 2016 (link)

Matrix for z(15,29)

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Found by the scaffold algorithm.

(396.544848489 seconds, score = 93, 6643565 recursive calls, max depth = 48)

lower bound = 93, submitted by Andrew Kay on July 26th, 2016 (link, raw)

Bound for z(26,27)

Searching for matrices of weight greater than 142, all but one scaffold was eliminated without search.

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

(1503.072408529 seconds, score = 0, 16870567 recursive calls, max depth = 21)

upper bound = 142, submitted by Andrew Kay on July 26th, 2016 (link)

Bound for z(26,27)

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

lower bound = 142, submitted on July 26th, 2016 (link)

Matrix for z(4,5 | 4,4)

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Found by the quotient matrix algorithm.

(622562.032240404 seconds, score = 70, 11635275344 recursive calls, max depth = 20)

weight = 70, submitted by Andrew Kay on July 26th, 2016 (link, raw)

Bound for z(24,26)

By deleting $5$ rows and $7$ columns from the finite projective plane of order 5.

lower bound = 129, submitted on July 18th, 2016 (link)

Bound for z(22,26)

By deleting $5$ rows and $9$ columns from the finite projective plane of order 5.

lower bound = 120, submitted on July 18th, 2016 (link)

Bound for z(21,25)

By deleting $6$ rows and $10$ columns from the finite projective plane of order 5.

lower bound = 112, submitted on July 18th, 2016 (link)

Matrix for z(15,28)

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Found by the scaffold algorithm.

(180414.627925918 seconds, score = 91, 1592500300 recursive calls, max depth = 47)

weight = 91, submitted by Andrew Kay on May 9th, 2016 (link, raw)