Abstract
Let L be a non-trivial finite linear space in which every line has n or n+1 points. We describe L completely subject to the following restrictions on n and on the number of points p: p≤n2+n−1 and n≥3; n2+n+2≤p≤n2+2n−1 and n≥3; p=n2+2n and n≥4; p=n2+2n+2 and n≥3; p=n2+2n+3 and n≥4.
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