Alphabet-Dependent Bounds for Pure Quantum $(r,ρ)$-Locally Recoverable Codes

A quantum $(r,ρ)$-locally recoverable code ($(r,ρ)$-qLRC) is a quantum code in which every qudit can be recovered from at most $r+ρ-1$ other qudits, even after $ρ-1$ additional erasures inside the recovery set. The bounds currently known for this class, namely the Singleton-like and the GG Singleton