In this paper we prove the existence of a complete cap of (Formula presented.) of size (Formula presented.), for each prime power (Formula presented.). It is obtained by projecting two disjoint Veronese varieties of (Formula presented.) from a suitable (Formula presented.) -dimensional projective space. This shows that the trivial lower bound for the size of the smallest complete cap of (Formula presented.) is essentially sharp.
Small complete caps in PG(4n + 1, q) / Cossidente, A.; Csajbok, B.; Marino, G.; Pavese, F.. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 55:1(2023), pp. 522-535. [10.1112/blms.12743]
Small complete caps in PG(4n + 1, q)
Marino G.;
2023
Abstract
In this paper we prove the existence of a complete cap of (Formula presented.) of size (Formula presented.), for each prime power (Formula presented.). It is obtained by projecting two disjoint Veronese varieties of (Formula presented.) from a suitable (Formula presented.) -dimensional projective space. This shows that the trivial lower bound for the size of the smallest complete cap of (Formula presented.) is essentially sharp.File in questo prodotto:
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