The embedding in \(\text{AG}(3,q)\) of \((0,2)\)-geometries with no planar nets (Q1763870)

A \((0,\alpha)\)-geometry \(S=({\mathcal P},{\mathcal B},I)\) is a connected linear space of order \((s,t)\) with the property that for every anti-flag \((P,L)\) the number \(\alpha(p,L)\) of lines of \(S\) through \(P\) intersecting \(L\) is equal to \(0\) or a constant \(\alpha\). In the paper under review, the author studies \((0,2)\)-geometries of order \((2^h-1,t)\) embedded in AG\((3,2^h)\) with no planar nets. Assuming \(t=2^h\), the author provides a complete classification.