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Non-containment of conics in untouchable sets of size $2q+1$
Conjecture on conic-free untouchable sets. An untouchable set of size $2q+1$ in $PG(2,q)$ may not contain a conic.
Conjectureopenfinite-geometry projective-planes untouchable-setsarXiv posted 2 days ago

Non-containment of conics in untouchable sets of size 2q+12q+12q+1