Caps in PG(n,q) with q even and n≥3

Let m2(n,q), m2′(n,q) be, respectively, the maximum value, the second largest value of k for which there exists a complete k-cap in PG(n,q). In this paper, the known upper bound on m2′(3,q), q even, q≥128, is improved. This new upper bound on m2′(3,q) is then used to improve the upper bounds on m2(n,q), q even, q≥128 and n≥4. However, only when q≥128,n=4 and n=5, the result of m2(n,q) is better than the result of S. Ferret and L. Storme.