Small complete caps in \rm PG(4n + 1, q)

2021/05/31 by Cossidente, Antonio, Csajbók, Bence, Marino, Giuseppe +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.14939

Abstract

In this paper we prove the existence of a complete cap of \rm PG(4n+1, q) of size 2(q²ⁿ⁺¹-1)/(q-1), for each prime power q>2. It is obtained by projecting two disjoint Veronese varieties of \rm PG(2n²+3n, q) from a suitable (2n²-n-2)-dimensional projective space. This shows that the trivial lower bound for the size of the smallest complete cap of \rm PG(4n+1, q) is essentially sharp.

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