MCDQLS(n) exists for all but a few n, based on constructions for idempotent MCQLS(n) and implying results for MCPQLS(n).
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The Existence of Diagonal Quantum Latin Squares with Maximum Cardinality
MCDQLS(n) exists for all but a few n, based on constructions for idempotent MCQLS(n) and implying results for MCPQLS(n).