Small complete caps in PG ( N , q ), q even

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 $q^{{N}\over{2}}$ is replaced by $\alpha q^{{N}\over{2}}$ with $\alpha \le {{1}\over{2}}$ , for N odd 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