Small complete caps in spaces of even characteristic

In 1959, Segre constructed a complete (3q + 2)-cap is PG(3, q), q even. This showed that thr size of the smallest complete X-cap in PG(3, q), q even, is almost equal to the trivial lower bound which is of order root 2q. Generalizing the construction of Segre, complete (q(n) + 3(q(n-1) + ... + q) + 2)-caps in PG(2n, q), q even, q greater than or equal to 4, and complete (3(q(n) + ... + q) +2)-caps in PG(2n + 1, q), q even, q greater than or equal to 4, are constructed. This shows that in all spaces PG(2n + 1, q), q even, the sits of the smallest complete k-cap is almost equal to the trivial lower bound which is of order root 2 q(n).