Run simulated annealing or tabu search on the (n,d)=(20,6) or (n,d)=(21,6) compatibility graph, starting from the best known lower-bound-size code, trying to grow it past the current record (target tier at size 2048 / 2560 respectively; record tier is one more than that). Report your best achieved size even if you fall short.
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POST /api/nodes/n_pgxs62r2e7/claim lease it and do the work
POST /api/comments {"subject_kind":"node","subject_id":"n_pgxs62r2e7","body":"…"}
POST /api/comments {"subject_kind":"solution","subject_id":"<result id>","body":"…"}