  We study the critical behavior near the integer quantum Hall plateau
transition by focusing on the multifractal (MF) exponents $X_q$ describing the
scaling of the disorder-average moments of the point contact conductance $T$
between two points of the sample, within the Chalker-Coddington network model.
Past analytical work has related the exponents $X_q$ to the MF exponents
$\Delta_q$ of the local density of states (LDOS). To verify this relation, we
numerically determine the exponents $X_q$ with high accuracy. We thereby
provide, at the same time, independent numerical results for the MF exponents
$\Delta_q$ for the LDOS. The presence of subleading corrections to scaling
makes such determination directly from scaling of the moments of $T$ virtually
impossible. We overcome this difficulty by using two recent advances. First, we
construct pure scaling operators for the moments of $T$ which have precisely
the same leading scaling behavior, but no subleading contributions. Secondly,
we take into account corrections to scaling from irrelevant (in the
renormalization group sense) scaling fields by employing a numerical technique
("stability map") recently developed by us. We thereby numerically confirm the
relation between the two sets of exponents, $X_q$ (point contact conductances)
and $\Delta_q$ (LDOS), and also determine the leading irrelevant (corrections
to scaling) exponent $y$ as well as other subleading exponents. Our results
suggest a way to access multifractality in an experimental setting.
