Abstract
We classify all representations of an arbitrary affine plane A of order q in a projective space PG(d,q) such that lines of A correspond with affine lines and/or plane q-arcs and such that for each plane q-arc which corresponds to a line L of A the plane of PG(d,q) spanned by the q-arc does not contain the image of any point off L of A.
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Thas, J.A., Van Maldeghem, H. Finite affine planes in projective spaces. Combinatorica 37, 283–311 (2017). https://doi.org/10.1007/s00493-014-3179-z
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DOI: https://doi.org/10.1007/s00493-014-3179-z