  We prove that the Kalton-Peck twisted sum $Z_2^n$ of $n$-dimensional Hilbert
spaces has GL-l.u.st.\ constant of order $\log n$ and bounded GL constant. This
is the first concrete example which shows different explicit orders of growth
in the GL and GL-l.u.st.\ constants. We discuss also the asymmetry constants of
$Z_2^n$.
