  A new lower bound for the maximal length of a multivector is obtained. It is
much closer to the best known upper bound than previously reported lower bound
estimates. The maximal length appears to be unexpectedly large for $n$-vectors,
with n>2, since the few exactly known values seem to grow linearly with vector
space dimension, whereas the new lower bound has a polynomial order equal to
n-1 like the best known upper bound. This result has implications for quantum
chemistry.
