You can search at Helpmefind.com, click on "Class" and select "Miniature" and "Mini-Flora" from the pop-up (then "Continue") then click on "Bloom" and select "White" and "Mauve & mauve-blend" ("Mauve" is the ARS color classification for lavender and purple roses, and it will give you a better list than if you selected "Lavender") from that pop-up (then "Continue") then click on "Search" on the right side of the page. This will give you a list of roses that meet your criteria as far as class and color are concerned.

Size is strange with minis and mini-floras. Some can be 3'+ tall. So when you say "ground cover" you'll have to be a little more specific on maximum height.

Some excellent vendors are Bridges Roses, Nor'East Mini Roses, Almost Heaven Roses, John's Miniature Roses, Rosemania.com.