  We work out the phase-space structure for a system of $n$ qubits. We replace
the field of real numbers that label the axes of the continuous phase space by
the finite field $\Gal{2^n}$ and investigate the geometrical structures
compatible with the notion of unbiasedness. These consist of bundles of
discrete curves intersecting only at the origin and satisfying certain
additional properties. We provide a simple classification of such curves and
study in detail the four- and eight-dimensional cases, analyzing also the
effect of local transformations. In this way, we provide a comprehensive
phase-space approach to the construction of mutually unbiased bases for $n$
qubits.
