A new family of small complete caps in $PG(N, q)$, $q$ even, is constructed. Apart from small values of either $N$ or $q$, it provides an improvement on the currently known upper bounds on the size of the smallest complete cap in $PG(N, q)$: for $N$ even, the leading term $q^{N/2}$ is replaced by $\alpha q^{N/2}$ with $\alpha <= 1/2$, for $N$ odd the leading term $3q^{(N-1)/2}$ is replaced by $\beta q^{(N-1)/2}$ with $\beta <= 5/2$.
Small complete caps in PG(N,q), q even
GIULIETTI, Massimo
2007
Abstract
A new family of small complete caps in $PG(N, q)$, $q$ even, is constructed. Apart from small values of either $N$ or $q$, it provides an improvement on the currently known upper bounds on the size of the smallest complete cap in $PG(N, q)$: for $N$ even, the leading term $q^{N/2}$ is replaced by $\alpha q^{N/2}$ with $\alpha <= 1/2$, for $N$ odd the leading term $3q^{(N-1)/2}$ is replaced by $\beta q^{(N-1)/2}$ with $\beta <= 5/2$.File in questo prodotto:
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