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The bad science matrix problem consists in finding, among all matrices A R^n n with rows having unit ² norm, one that maximizes (A) = 12ⁿ ₗ \-₁, ₁\ⁿ \|Ax\|_. Our main contribution is an explicit construction of an n n matrix A showing that (A) ₂ (n+1), which is only 18% smaller than the asymptotic rate. We prove that every entry of any optimal matrix is a square root of a rational number, and we find provably optimal matrices for n 4.
Albors et al. (Thu,) studied this question.
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