  For non-binary codes the Elias bound is a good upper bound for the asymptotic
information rate at low relative minimum distance, where as the Plotkin bound
is better at high relative minimum distance. In this work, we obtain a hybrid
of these bounds which improves both. This in turn is based on the anticode
bound which is a hybrid of the Hamming and Singleton bounds and improves both
bounds.
  The question of convexity of the asymptotic rate function is an important
open question. We conjecture a much weaker form of the convexity, and we show
that our bounds follow immediately if we assume the conjecture.
