Lp Linear discrepancy of totally unimodular matrices Original Research Article

Let p set membership, variant [1, ∞[ and cp = maxa set membership, variant [0, 1]((1 − a)ap + a(1 − a)p)1/p. We prove that the known upper bound lindiscp(A) less-than-or-equals, slant cp for the Lp linear discrepancy of a totally unimodular matrix A is asymptotically sharp, i.e.,imageWe estimate image for some εp set membership, variant [0, 2−p+2], hence image. We also show that an improvement for smaller matrices as in the case of L∞ linear discrepancy cannot be expected. For any image we give a totally unimodular (p + 1) × p matrix having Lp linear discrepancy greater than image.