  This short paper presents a necessary condition for Byzantine $k$-set
agreement in (synchronous or asynchronous) message-passing systems and
asynchronous shared memory systems where the processes communicate through
atomic single-writer multi-reader registers. It gives a proof, which is
particularly simple, that $k$-set agreement cannot be solved $t$-resiliently in
an $n$-process system when $n \leq 2t + \frac{t}{k}$. This bound is tight for
the case $k=1$ (Byzantine consensus) in synchronous message-passing systems.
