I'm a furniture removalist, so from work I've got hessian sheets (7'x4') that we lay out on the concrete at the 25m line (folded in half in the individual pistol booths), or opened out fully right across the line on the gravel when we're out in the open at the gun club. If you are going to use sheets from home and out in the open, take a few and spread them out fully, weigh the corners down (against lifting by breezes or the wind), take a few practice shots at the target, watching the cases eject onto the sheets and adjust your position on the sheets until you have the cases landing squarely on the sheets. You'll be going home with more empty cases than not at every position / line that you shoot from.
Don't be disappointed if you can't find 1 or 2 cases. Work your way around the sheet edges as sometimes the empties land awkwardly and roll away, but they won't be too far from the sheet edges or just underneath.
Fold your sheets up, and take them home until next time. I leave the hessian at the club for the next guy(s) to use. They don't go missing, but your sheets will.