Let's I have a method to remove duplicates in an integer Array

 public int[] RemoveDuplicates(int[] elems)
    {
        HashSet<int> uniques = new HashSet<int>();
        foreach (int item in elems)
            uniques.Add(item);
        elems = new int[uniques.Count];
        int cnt = 0;
        foreach (var item in uniques)
            elems[cnt++] = item;
        return elems;
    }

How can I make this generic such that now it accepts a string array and remove duplicates in it? How about a double array? I know I am probably mixing things here in between primitive and value types. For your reference the following code won't compile

 public List<T> RemoveDuplicates(List<T> elems)
        {
            HashSet<T> uniques = new HashSet<T>();
            foreach (var item in elems)
                uniques.Add(item);
            elems = new List<T>();
            int cnt = 0;
            foreach (var item in uniques)
                elems[cnt++] = item;
            return elems;
        }

The reason is that all generic types should be closed at run time. Thanks for you comments