  We analyze and implement the Local Analytic Sector Subtraction (LASS) scheme
for handling infrared singularities in next-to-next-to-leading order (NNLO)
calculations in perturbative QCD. We examine the key aspects of the scheme
including sector function construction, singular limit parametrization,
subtraction counterterm derivation, and integration techniques. As a
proof-of-concept, we numerically implement LASS for the process $e^+e^-
\rightarrow 3$ jets. In this study we examine the limiting behavior of
subtraction terms for real-virtual contribution and explicitly demonstrate the
pole cancellation of the double-virtual contribution. Differential cross
sections are computed for several event shape observables, showing the
stability and efficiency of LASS scheme. This work lays the foundation for
developing an automated tool for NNLO QCD calculations using this promising
scheme.
