Small Complete Caps From Singular Cubics

New families of complete caps in finite Galois spaces are obtained. For most pairs (N, p(h)) with h > 8 and N equivalent to 0 (mod 4), they turn out to be the smallest known complete caps in AG(N, p(h)). Our constructions rely on the bicovering properties of certain plane arcs contained in plane cubic curves with a cusp. (C) 2013 Wiley Periodicals, Inc.