Parameterized System.Type Variable in C#

I am trying to make a factory class in C# that returns objects that are or extend a certain base type. I need to instantiate a new instance of this type every time I call getInstance() on the factory, so I really only want to accept and store the type itself. In Java I have used the Class<? extends Base> to hold the class to create and then called getInstance() on it.

I understand how to use the Activator class in C# to create new object from a System.Typebut the part I'm not sure about is the constraint on the class type. I want to be able to only accept Types that are or extend the base class. I realize that I could change the setter on the factory to accept an actual object of the base type then retrieve the type from it, but I didn't really want to instantiate an entire object just to retrieve a Type variable.

Below is a little example Java program just to demonstrate what I need, in case my question is not clear. Is there any way to do this in C#?

class Program {
   public static void main(String[] args) throws InstantiationException, IllegalAccessException {
         Factory.setClass(Base.class);
         Base b = Factory.getInstance();
         b.Print();

         Factory.setClass(Child.class);
         b = Factory.getInstance();
         b.Print();
      }
}

class Factory {
   private static Class<? extends Base> type;

   // What I want to do in C#.
   public static void setClass(Class<? extends Base> newType) {
      type = newType;
   }

   // What I don't want to have to do in C#.
   public static void setClassFromObject(Base newTypeObject) {
      type = newTypeObject.getClass();
   }

   public static Base getInstance() throws InstantiationException, IllegalAccessException {
      return type.newInstance();
   }
}

class Base {
   public void Print() {
      System.out.println("Hello from base.");
   }
}

class Child extends Base {
   @Override
   public void Print() {
      System.out.println("Hello from child.");
   }
}