Hard to answer this (it wasn’t the point I was making!) without defining how one is using “design” and “randomness”.
The second (“randomness”) is easier: if we take a proper scientific definition in the sense of “unprediuctable” or “of unknown cause” (ie, treat “randomness” as “ignorance”), then science does not study randomness… except that en masse, such random events form statistical patterns that can be studied scientifically and methematically - that was Maxwell’s great breakthrough.
It’s literally a textbook case of contingencies being abstracted in order to predict similar events.
“Design” turns out to be a weasel word, as the thread has shown. Theologically, the very presence of order is a hallmark of design (as Thomas Aquinas argued), and so the laws themselves are designed.
Taken of individual things, such as species of life, then contingency rules: we are looking at something unique as being possibly designed, and by analogy with human design, innovation and individuality is usually a mark of design: a ball might be accidental, but a Ferrari isn’t.
Incidentally, one indicator that the laws are designed might be that they themselves are, ultimately, contingent - hence the interest in the fine-tuning of cosmological constants. The laws act everywhere in a general way, but are hard to explain themselves (a huge thread on BioLogos abouyt that currently - “Where do physical laws come from.”
What I’m getting at here is that samne cointrast between repeatable pattern and contingency. To study design scientifically is to abstract it to some kind of pronicples, ideally mathematical. This is what ID people like Bill Dembski have attempted to do, without persuading the world - ultimately, perhaps, because it remains true that randomness and design produce similar statistical signatures, ie they are highly contingent.
So just as “randomness” can only be handles scientifically via statistics (which turns randomness into an abstracted pattern, hiding its randomness, ie its actual causes), in the same way one would expect any mathematical principles potentially to be found in design to transform the contingency of design into just another statistical pattern.
So I’m coming round to thinking that other, non scientific, human epistemologies must tackle the question of design.