What attractive, flowering groundcovers that grow no taller than
6" (under 3" would be best) would you recommend that will grow well
under these conditions:

I live in Riverside, California (about 60 miles east of Los Angeles).
I'm in USDA Zone 8b or Sunset Zone 19.

The summer high-temperatures may get up to 115 degrees
The winter low-temperatures may get down to 15 degrees.

One-third of my garden is partly-shaded by a deciduous tree from March
through December but the rest of my garden is in full-sun.