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z(12,23) = 66

Searching for matrices of weight greater than 66, all but 14 scaffolds were eliminated without search.

Scaffold: $p=5$, $q=2$, $\mathbf{m}=(2,2,2,2,1)$, $\mathbf{n}=(5,5)$, $m_O=0$, $n_O=7$.

(7.111747164 seconds, score = 0, 48064 recursive calls, max depth = 31)

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

(4.89448E-4 seconds, score = 0, 0 recursive calls, max depth = 0)

Scaffold: $p=5$, $q=2$, $\mathbf{m}=(2,2,2,2,1)$, $\mathbf{n}=(4,4)$, $m_O=0$, $n_O=9$.

(0.002888635 seconds, score = 0, 0 recursive calls, max depth = 0)

Scaffold: $p=5$, $q=2$, $\mathbf{m}=(2,2,2,2,1)$, $\mathbf{n}=(5,4)$, $m_O=0$, $n_O=8$.

(59.929840804 seconds, score = 0, 437549 recursive calls, max depth = 33)

Scaffold: $p=5$, $q=2$, $\mathbf{m}=(2,2,2,1,1)$, $\mathbf{n}=(4,4)$, $m_O=1$, $n_O=9$.

(0.001922311 seconds, score = 0, 0 recursive calls, max depth = 0)

Scaffold: $p=5$, $q=2$, $\mathbf{m}=(2,2,2,1,1)$, $\mathbf{n}=(5,4)$, $m_O=1$, $n_O=8$.

(39.386142653 seconds, score = 0, 276397 recursive calls, max depth = 34)

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

(0.507494947 seconds, score = 0, 3417 recursive calls, max depth = 26)

Scaffold: $p=5$, $q=3$, $\mathbf{m}=(2,2,2,1,1)$, $\mathbf{n}=(4,4,4)$, $m_O=0$, $n_O=5$.

(10.782118677 seconds, score = 0, 80450 recursive calls, max depth = 29)

Scaffold: $p=5$, $q=3$, $\mathbf{m}=(2,2,2,1,1)$, $\mathbf{n}=(5,4,4)$, $m_O=0$, $n_O=4$.

(1.462763004 seconds, score = 0, 11461 recursive calls, max depth = 27)

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

(16.265699132 seconds, score = 0, 117996 recursive calls, max depth = 31)

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

(2.78527E-4 seconds, score = 0, 0 recursive calls, max depth = 0)

Scaffold: $p=6$, $q=2$, $\mathbf{m}=(2,2,2,1,1,1)$, $\mathbf{n}=(5,4)$, $m_O=0$, $n_O=7$.

(52.796655721 seconds, score = 0, 369092 recursive calls, max depth = 32)

Scaffold: $p=6$, $q=2$, $\mathbf{m}=(2,2,2,1,1,1)$, $\mathbf{n}=(6,4)$, $m_O=0$, $n_O=6$.

(0.483403617 seconds, score = 0, 3097 recursive calls, max depth = 26)

Scaffold: $p=6$, $q=2$, $\mathbf{m}=(2,2,2,1,1,1)$, $\mathbf{n}=(4,4)$, $m_O=0$, $n_O=8$.

(0.179921749 seconds, score = 0, 986 recursive calls, max depth = 28)

upper bound = 66, submitted by Andrew Kay on April 22nd, 2016 (link)

By adding a column of weight 1 to z(12,22).

lower bound = 66, submitted on April 22nd, 2016 (link)

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