Implement a function that performs a single value function update using tile coding with a properly adjusted step size.

In tile coding, multiple overlapping tilings each activate exactly one tile for a given state. This means the total number of active features equals the number of tilings. If the step size is not adjusted to account for this, learning becomes unstable or overly slow.

Your function should:

1. Accept a base learning rate, the number of tilings, a weight vector, a list of active tile indices for the current state, and a target value.
2. Compute an adjusted step size that accounts for the number of tilings.
3. Compute the current value estimate as the sum of weights at the active tile indices.
4. Update only the weights corresponding to active tiles using the adjusted step size and the prediction error (target minus current estimate).
5. Compute the value estimate after the update.

Return a dictionary with keys: 'adjusted_alpha' (the adjusted step size), 'prediction_before' (value estimate before update), 'prediction_after' (value estimate after update), and 'updated_weights' (the full weight vector after update). All numerical values should be rounded to 4 decimal places.