Abstract
A d-dimensional dual arc in PG(n, q) is a higher dimensional analogue of a dual arc in a projective plane. For every prime power q other than 2, the existence of a d-dimensional dual arc (d ≥ 2) in PG(n, q) of a certain size implies n ≤ d(d + 3)/2 (Theorem 1). This is best possible, because of the recent construction of d-dimensional dual arcs in PG(d(d + 3)/2, q) of size ∑d−1 i=0 q i, using the Veronesean, observed first by Thas and van Maldeghem (Proposition 7). Another construction using caps is given as well (Proposition 10).
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