On counterexamples to the Mertens conjecture

We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to \(\approx \exp (1.96 \times 10^{19})\) $\approx exp(1.96\times {10}^{19})$ , which is significantly below the conjectured value of \(\approx \exp (5.15 \times 10^{23})\) $\approx exp(5.15\times {10}^{23})$ by Kotnik and van de Lune (Exp Math 13:473–481, 2004).