This is a slightly adapted version of Vincentās very handy project with some added packages and a couple of tweaks to the table.
Please note that not all datasets could be parsed correctly, with some type-specific issues for non-data.frame datasets such as plyr::ozone which is an array with dimensions 24 24 72.
This shows all 1920 datasets.
This subset contains 803 datasets with Rows <= 100 & Cols <= 10.
This subset contains 35 datasets with Cols > Rows.
Defining high-dimensionality is hard but this seems like a place to start.
This subset contains 89 datasets with Rows >= 10000.