Small complete caps inPG(N,q),qeven
Massimo Giulietti · Journal of Combinatorial Designs · 2006
Abstract A new family of small complete caps inPG(N,q),qeven, is constructed. Apart from small values of eitherNorq, it provides an improvement on the currently known upper bounds on the size of the smallest complete cap inPG(N,q): forNeven, the leading term$q^{{N}\over{2}}$ is replaced by$\alpha q^{{N}\over{2}}$ with$\alpha \le {{1}\over{2}}$ , forNodd the leading term$3q^{{N-1}\over{2}}$ is replaced by$\beta q^{{N-1}\over{2}}$ with$\beta \le {{5}\over{2}}$ . © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 420–436, 2007