  We consider the bit-probe complexity of the set membership problem, where a
set S of size at most n from a universe of size m is to be represented as a
short bit vector in order to answer membership queries of the form "Is x in S?"
by adaptively probing the bit vector at t places. Let s(m,n,t) be the minimum
number of bits of storage needed for such a scheme. Several recent works
investigate s(m,n,t) for various ranges of the parameter; we obtain
improvements over some of the bounds shown by Buhrman, Miltersen,
Radhakrishnan, and Srinivasan (2002) and Alon and Feige (2009).
