Reduce space between icons on home screen without changing icon size
Reducing the gap also reduces the sizes. If you are using the default launcher Trebuchet, you should also see Custom in the Grid Size settings. Clicking it allow to set the number of icons per columns and rows. Select a high number for colums and rows.




Confirm your choice, then go back to the Home screen and rearrange the icons. You will be able to fit as many icons as you selected in the settings. The gap between them will be reduced.



If 7x7 is not enough, you can use other launchers. Nova launcher for example allow a 12x12 grid.

Note: I am not related to Trebuchet nor Nova launchers developers.