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