$PG(N,q)$，$q$甚至完全帽的新的归纳构造
New inductive constructions of complete caps in $PG(N,q)$, $q$ even
摘要：
描述了$PG(N,q)$，甚至$q$中的一些新的小完整帽族。利用归纳论证，将任意维射影空间中的小完备帽的构造问题归结为平面上的同样问题。本文构造的帽对目前已知的$PG(N,q),$ $N\geq 4,$中对于所有$q\geq 2^{3}.$的最小完全帽的大小的上界提供了改进。特别地，对于$q$平方的无限值，包括$ q=2^{2Cm},$ $C\geq 5,$ $m\geq 3;$ for $q=2^{Cm},$ $C\geq 5,$ $m\geq 9,$ with $C,m$ odd;以及对于所有$q\leq 2^{18}.$，
英文摘要：
Some new families of small complete caps in $PG(N,q)$, $q$ even, are described. By using inductive arguments, the problem of the construction of small complete caps in projective spaces of arbitrary dimensions is reduced to the same problem in the plane. The caps constructed in this paper provide an improvement on the currently known upper bounds on the size of the smallest complete cap in $PG(N,q),$ $N\geq 4,$ for all $q\geq 2^{3}.$ In particular, substantial improvements are obtained for infinite values of $q$ square, including $ q=2^{2Cm},$ $C\geq 5,$ $m\geq 3;$ for $q=2^{Cm},$ $C\geq 5,$ $m\geq 9,$ with $C,m$ odd; and for all $q\leq 2^{18}.$
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
