We show that, for a standard continuously polydisperse model with particle-diameter distribution $P\left(\sigma \right)\propto {\sigma }^{-3}$ and polydispersity index $\mathrm{\Delta }$, employing a combination of standard SWAP moves and transient degree of freedom (TDOF) moves during a Lubachevsky-Stillinger-like particle-growth process dramatically increases the generated packings' jamming densities ${\varphi }_{\mathrm{J}}\left(\mathrm{\Delta }\right)$ and coordination numbers $Z_{\mathrm{J}}\left(\mathrm{\Delta }\right)$, for a wide range of $\mathrm{\Delta }$. The fractional increase in ${\varphi }_{\mathrm{J}}\left(\mathrm{\Delta }\right)$ obtained by employing these moves first increases rapidly with $\mathrm{\Delta }$, then plateaus at $6–7\%$ over the range $0.1\lesssim \mathrm{\Delta }\le 0.5$; the obtained ${\varphi }_{\mathrm{J}}$ are as high as 0.747 (for $\mathrm{\Delta }=0.50$). These density increases are achieved without producing clearly noticeable crystallization or increased fractionation, despite the fact that the packings are quite hyperstatic for all $\mathrm{\Delta }>0$. SWAP and TDOF moves also reduce packings' rattler populations by as much as 99% and increase their bulk moduli by as much as 80%.

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• Jamming
• Granular solids
• Monte Carlo methods