On MDI like you
@Simon789 used to like to be in the 6s minimum. Even now, as an adult and with a pump, I'm always careful about my blood sugar before going to bed. Safety is the most important thing for me.
I'd never correct a 6 at bedtime. if I feel my blood sugar might be on the way up or I'm worried that my evening meal is still active, then I test around 2am to see what's happening.
I seem to remember being told not to go to bed below 7 or 8 when I was younger. If you're concerned, then your DSN should be able to,advise you about what a sensible number would be for you. It depends a lot on your age and how the basal affects you.