  We consider the problem of non-adaptive noiseless group testing of $N$ items
of which $K$ are defective. We describe four detection algorithms: the COMP
algorithm of Chan et al.; two new algorithms, DD and SCOMP, which require
stronger evidence to declare an item defective; and an essentially optimal but
computationally difficult algorithm called SSS. By considering the asymptotic
rate of these algorithms with Bernoulli designs we see that DD outperforms
COMP, that DD is essentially optimal in regimes where $K \geq \sqrt N$, and
that no algorithm with a nonadaptive Bernoulli design can perform as well as
the best non-random adaptive designs when $K > N^{0.35}$. In simulations, we
see that DD and SCOMP far outperform COMP, with SCOMP very close to the optimal
SSS, especially in cases with larger $K$.
