In this paper the notion of strongly resolving markets with respect to the positive basis of a minimal lattice-subspace $Y$ of $\Bbb R^m$ is defined. It is proved that if the number of securities is less than half the dimension of $Y$, then not a single (non-trivial) option can be replicated. This result extends already known results regarding the notion of a market being strongly resolving. Both theoretical and computational methods are provided in order to establish criteria for the characterization of markets that do not replicate any option.