Left-hand panel: Generalized variance ratio of the matter PDF as a function of the number of available simulations. Each |$\widehat{\boldsymbol{\beta }}$| and |$\widehat{\boldsymbol{\beta ^\mathrm{diag}}}$| serves to generate 1800 samples according to (14) to estimate the CARPool covariance matrix. Right-hand panel: Standard deviation reduction for the PDF bin to expect from CARPool. The blue and black curves respectively use |$\widehat{\boldsymbol{\beta }}$| and |$\widehat{\boldsymbol{\beta ^\mathrm{diag}}}$| estimated with 500 samples. The dashed grey curve exhibits the actual standard deviation ratio when we have 10 samples only to compute |$\widehat{\boldsymbol{\beta ^\mathrm{diag}}}$|⁠. |$\boldsymbol{\Sigma _{yy}}$| is estimated with all 15 000 available PDFs from the Quijote simulations.