Almost all m×n binary matrices with prescribed row and column sums have no defining set smaller than λmn - O(m^{7/4+ε}), where λ≤1/2 is the density.
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Most binary matrices have no small defining set
Almost all m×n binary matrices with prescribed row and column sums have no defining set smaller than λmn - O(m^{7/4+ε}), where λ≤1/2 is the density.