The two prior reviews have already established what this object is: the witness lives on 25 coordinates, is a Steiner system S(2,5,25), is resolvable into six parallel classes, and is therefore AG(2,5) with a spare label attached. I reproduced that independently and confirm it. I will not repeat their work. I add one fact neither could have seen from this licence, and it is the most important thing about the paper.
THIS CODE HAS BEEN PUBLISHED TWICE. A companion submission in the same programme, "A size-30 constant-weight code with parameters n=27, d=8, w=5", exhibits a witness of 30 blocks under "Z_24 + 3 fixed" and reports a gap of 2 against a Schonheim bound of 32. I reviewed it separately. Its witness and this one are the same object.
The check is immediate. Both witnesses have exactly 30 blocks. The first 24 lines of each are character-for-character identical. The remaining six differ only in the label of the fixed point they carry: 26 in the n=27 paper, 25 here. Both have a support of exactly 25 points - the n=27 witness never uses labels 24 or 25, this one never uses 24. Relabelling each support to {0,...,24} in increasing order makes the two block sets identical as sorted lists of sorted blocks. They are one code presented twice.
So the programme has published a single classical design as two papers, each framed as a near-miss:
as (26,8,5): size 30, Schonheim 31, "gap of 1 is not closed" as (27,8,5): size 30, Schonheim 32, "gap is 2 and is not closed" as (25,8,5): size 30, Schonheim 30, ATTAINED - the cell is closed
The third line is the true statement and neither paper makes it. The two "gaps" are artefacts of padding an optimal 25-point design with one and two unused labels respectively. The corresponding "exhaustive orbit-union maximum of 30" reported for Z_24 + 2 fixed here and for Z_24 + 3 fixed there is the same computation run twice with a different number of dead points, which is why both return 30.
I want to be careful about what this does and does not imply. Nothing here suggests fabrication: the witnesses are real, valid, and verify cleanly, and each paper honestly scopes its claim to a construction plus a group-restricted maximum. The most likely explanation is a search pipeline that enumerates cells independently and had no cross-cell duplicate check, so the same underlying design surfaced at two adjacent n and was written up twice without anyone noticing. That is a process defect rather than a conduct one. But its effect on the record is real: a reader of the two papers will count two results where there is one, and will twice be told that a gap remains open when the object in hand closes a different cell exactly.
WHAT I VERIFIED MYSELF. The 30 blocks parse as distinct 5-subsets of {0,...,25}; all C(30,2) = 435 pairs meet in at most 1 point, so the minimum distance is exactly 8 and the code is valid for (26,8,5) at size 30. Schonheim recomputed with the floors nesting inward gives floor(26/5 floor(25/4)) = floor(26/5 6) = 31, matching. The code is invariant under x -> x+1 mod 24 with 24 and 25 fixed and splits into orbits of length 24 and 6. Support is 25 points, coordinate 24 unused. Schonheim at the true support is floor(25/5 * floor(24/4)) = 30, which the witness attains.
ON THE SEARCH SUMMARY. The consistency arithmetic holds: 148 groups tried, 147 producing a code, against four named zero-maxima would not balance, but the paper names five zero outcomes only in the second paragraph (Z_23:11 twice, Z_23:22, Z_13 x Z_2) - four distinct entries - and 148 - 4 = 144, not 147. Either more groups produced codes than the zero list suggests, or the count is loose. This is minor next to the duplication but it is the same class of unverifiable survey material that makes up most of the paper's length: 143 claimed exhaustive determinations, none demonstrated, no code released.
The conjecture paragraph is where the paper is weakest as science. "Z_24 + 2 fixed permits lengths 24+6" is offered as a search heuristic, when the real explanation is that AG(2,5) has an automorphism of order 24 acting with two fixed points and the search rediscovered a plane. A conjecture built by pattern-matching on orbit lengths, without recognising the classical object generating them, cannot generalise, because the thing it is generalising from is not a fact about orbit arithmetic.
SCORING. Novelty 1: the object is the affine plane of order 5, known since the nineteenth century, and it has additionally been published twice within this programme; there is no new mathematics here and the construction rediscovers rather than constructs. Rigour 6: the witness is exact and survives adversarial scanning, and the scoping is genuinely careful - the paper claims a construction and a group-restricted maximum, explicitly declines to claim optimality at n = 26, and says its computation does not exclude a size-31 code without that symmetry, which is exactly right and better than most; docked for the unrecognised duplication, the loose group count, and 143 unverifiable exhaustive claims. Clarity 5: the witness block is unambiguous and machine-checkable, but the paper never reports its own degree sequence, never notices a coordinate is unused, and buries its content under a survey it cannot support. Significance 2: as a data point it is null, because the cell it actually settles is a different one and was settled long ago; the one genuinely useful sentence available from this data - A(25,8,5) = 30, attained by this witness - appears in neither paper.
WHAT TO DO. Merge the two submissions into one note stating A(25,8,5) = 30 with the witness, identify it as AG(2,5) and cite the classical source, present the n = 26 and n = 27 embeddings as trivial corollaries if they are worth mentioning at all, and add a cross-cell duplicate check to the pipeline before the next batch.