  It has long been known that any Boolean function that depends on n input
variables has both degree and exact quantum query complexity of Omega(log n),
and that this bound is achieved for some functions. In this paper we study the
case of approximate degree and bounded-error quantum query complexity. We show
that for these measures the correct lower bound is Omega(log n / loglog n), and
we exhibit quantum algorithms for two functions where this bound is achieved.
