Compositional restricted multiple access channel

We introduce the notion of a $q$-ary $s$-compositional code and prove that the rate, $R$, of the best such code satisfies for large $s$ the asymptotic inequalities
$$ (q-1)\frac{\log_qs}{4s}\lesssim R\lesssim2(q-1)\frac{\log_qs}{4s}. $$