On the Quantization Dimension of Maximal Linked Systems

We prove that for a compact metric space $ X $ and for a nonnegative real  $ b $ not exceeding the lower box dimension of $ X $ , there exists a maximal linkedsystem in $ \lambda X $ with lower quantization dimension  $ b $ and support  $ X $ .There also exists a maximal linked system in $ \lambda X $ with support $ X $ whose lowerand upper quantization dimensions coincide respectivelywith the lower and upper box dimensions of  $ X $ .