Abstract
Ak-cap in PG(3,q) is a set of k points, no three of which are collinear. A k-cap is calledcomplete if it is not contained in a (k+1)-cap. The maximum valuem 2(3, q) ofk for which there exists a k-cap in PG(3,q) is q2+1. Letm 2(3, q) denote the size of the second largest complete k-cap in PG(3,q). This number is only known for the smallest values of q, namely for q=2, 3,4 (cf. [2], pp. 96–97 and [3], p. 303). In this paper we show thatm 2(3,5)=20. We also prove that there are, up to isomorphism, only two complete 20-caps in PG(3,5) and determine their collineation groups.
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In memoriam Giuseppe Tallini
Work done within the activity of GNSAGA of CNR and supported by MURST.
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Abatangelo, V., Korchmaros, G. & Larato, B. Classification of maximal caps in PG(3,5) different from elliptic quadrics. J Geom 57, 9–19 (1996). https://doi.org/10.1007/BF01229246
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DOI: https://doi.org/10.1007/BF01229246