European Journal of Combinatorics, 22 (2001), 135--143.
A family of caps constructed by Ebert, Metsch and T. Szönyi results from projecting a Veronesian or a Grasmannian to a suitable lower-dimensional space. We improve on this construction by projecting to a space of much smaller dimension. More precisely we partition PG(3r-1,q) into a (2r-1)-space, an (r-1)-space and qr-1 cyclic caps, each of size (q2r-1)(q-1). We also decide when one of our caps can be extended by a point from the (2r-1)-space or the (r-1)-space. The proof of the results uses several ingredients, most notably hyperelliptic curves.
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