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z(6,7) = 18

Every finite projective plane incidence matrix has a minor isomorphic to Matrix 1756, due to the non-degeneracy axiom.

submitted by Andrew Kay on April 23rd, 2016 (link)

By the convex optimisation bound with 4 columns of weight 3 and 3 columns of weight 2.

upper bound = 18, submitted on April 22nd, 2016 (link)

111
111
111
111
111
111

lower bound = 18, submitted on April 22nd, 2016 (link, raw)

Related: Comment 2089

Delete one row from the Fano plane.

lower bound = 18, submitted on April 22nd, 2016 (link)

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