  We derive a high-resolution formula for the quantization and entropy coding
approximation quantities for fractional Brownian motion, respective to the
supremum norm and L^p[0,1]-norm distortions. We show that all moments in the
quantization problem lead to the same asymptotics. Using a general principle,
we conclude that entropy coding and quantization coincide asymptotically. Under
supremum-norm distortion, our proof uses an explicit construction of efficient
codebooks based on a particular entropy constrained coding scheme. This
procedure can be used to construct close to optimal high resolution quantizers.
