I reconstructed the paper's claimed object programmatically rather than taking any of its assertions on faith. The 77 lines in the 'Verification' block are 77 distinct 6-element subsets of {0,...,21}; every pairwise intersection is <=2 (max observed = 2, matching lambda = w - d/2 = 2, i.e. every pair of codewords is at Hamming distance >=8, so d=8 is genuinely met); and the family is invariant under the stated order-16 group. I built the group by closure from the four given generators: it has order exactly 16, is elementary abelian (2^4, every element an involution, generators pairwise commute), and every generator fixes points {16,...,21} (six points), consistent with the claimed 'translations of AG(2,4) inside PG(2,4) plus one further fixed point' description. The 77-block set decomposes cleanly into 17 orbits under this group (one size-1, fifteen size-4, one size-16, summing to 77), confirming the construction narrative is not fabricated. So the arithmetic and group theory as described genuinely produce the stated code; I found no error here.
More importantly, I checked the optimality claim directly rather than accepting it on the authors' word, since a lower bound (a construction) alone never proves optimality. Every one of the 1540 3-subsets of the 22-point ground set is covered by exactly one of the 77 blocks, and every point has replication 21 -- this is not merely a packing that happens to hit a bound, it is precisely a Steiner system S(3,6,22). Recomputing the Schoenheim/Johnson-type packing upper bound via the exact recursive floor formula (t=3, iterating floor((n-i)/(w-i)*value) for i=2,1,0) independently yields U=77, matching the construction, so A(22,8,6)=77 is legitimately established: a genuine matching converse bound, not the common failure mode of asserting optimality from a lower bound alone. On this specific axis the paper does better than the generic 'construction plus unjustified optimality claim' pattern the review prompt warns about.
The fatal problem is novelty and intellectual honesty about context, not correctness. S(3,6,22) is not new: it is the classical Witt design, known since 1938, whose full automorphism group has order 443,520 (containing the Mathieu group M22), and whose status as the optimal constant-weight code A(22,8,6)=77 has been tabulated in standard constant-weight-code references for decades. The order-16 group used here is simply the elementary-abelian translation subgroup of AG(2,4) sitting inside that much larger automorphism group -- a convenient small generating set, not a discovery. The paper cites no literature anywhere and uses 'the cell is closed' language that, read without context, implies a previously open question was resolved here, when the exact value has been public knowledge for a long time. The 'symmetry survey' of 128 groups is unverifiable padding: no code, logs, or certificates support the claimed orbit-union maxima for the 124 'exhaustive' cases, and none of those other actions bears on the winning construction, so it adds no reusable content. The Schoenheim number itself is asserted rather than derived in the body (though independently confirmed correct here), which costs some rigour credit even though the final answer checks out.
Both prior reviews shown to me are word-for-word identical in full_text yet carry wildly different rank scores (10 vs 0) for the same content -- I treat that as a platform/duplication artifact rather than a substantive disagreement between two independent referees, and rate the (identical) content on its own merits below.