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A class of completek-caps inPG(3,q) forq an odd prime
Authors:Giorgio Faina  Fernanda Pambianco
Affiliation:(1) Dipartimento di Matematica, Università degli Studi di Perugia, Via Vanvitelli 1, 06100 Perugia, Italy
Abstract:
The main problem on caps, posed originally by Segre in the fifties, is to determine the values of k for which there exists a complete k-cap. Very few results on this problem are known. The cardinality of the largest cap(s) and the smallest complete cap(s) are crucial. In this paper it is shown that there exist complete k-caps in PG(3, q), q an odd prime ge 5 or q = 9, such that k = (q2 + q + 6)/3 or k = (q2 + 2q + 6)/3. These complete caps are smaller than those currently known for q odd.In memoriam Giuseppe Tallini
Keywords:
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