ZarankiewiczDB,

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Matrix for z(16,30)

1111111
111111
1111111
111111
1111111
111111
1111111
111111
111111
111111
111111
111111
11111
111111
111111
1111111

Found by the scaffold algorithm.

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

Matrix for z(15,30)

1111111
111111
1111111
111111
1111111
111111
111111
111111
111111
111111
111111
111111
111111
1111111
1111111

Found by the scaffold algorithm.

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

Matrix for z(14,30)

1111111
1111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
1111111
1111111
1111111

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)

111222
121212
122112
121221
11212
11122
11221

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)

111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
1111111
1111111

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)

111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
1111111
1111111
1111111

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)

1111
1111
1111
1111
1111
1111
111
111
111
111
1111
1111
111
111
1111
111
111
111
1111
111

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)

111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
111111
11111
1111111
1111111

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)