Research log — Linear covering codes of radius two

2026-08-16

• Ben Green, 100 Open Problems, Problem 40 — $1\le f(2)\le 1.4238$; unknown whether $f(2)=1$.
• Davydov–Marcugini–Pambianco, arXiv:2511.02542v1, Table 5.1 — documented $\ell_2(10,2)\le 51$, density $1327/1024$; also $\ell_2(8,2)\le 26$, $\ell_2(9,2)\le 39$. Named in the recovered witness_r10_n50.json.
• Kaikkonen–Rosendahl 51-column seed used by q1 search (named in WALKTHROUGH.md and witness JSON). The explicit 51-column hex listing was not recovered as a separate file.