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Jul 3, 2018 at 16:40 comment added Mare @JohannesHahn Thanks for your answer. It will probably take me some time to understand it in every detail. Sadly I think $r=3,s=4,q=5$ might be the first really interesting case... I think about adding another restriction to make the number much smaller, but probably it will get much more complicated.
Jul 3, 2018 at 16:00 comment added Johannes Hahn If my heurestic is right, the number of isomorphism classes is bounded below by some double-exponential of the form $q^{O(r^{3s})}$ (see the newest edit to my answer). Even for your smallish numbers, this will make it impossible to actually enumerate all isomorphism classes. The only way out is probably to use a coarser equivalence relation than isomorphism.
Jul 2, 2018 at 0:01 answer added Johannes Hahn timeline score: 4
Jul 1, 2018 at 21:08 comment added Johannes Hahn How fast is "quick" ? Do you already have an algorithm which you want to beat?
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