Mixed partitions of PG\((5,q)\)
This paper considers the problem of partitioning finite projective space into objects of given different types. Corollary 5. The projective space \(PG(5,q)\) can be partitioned into two planes and \(q^3-1\) quadric Veronesians. Moreover, if \(q\) is a square, then \(PG(5,q)\) can be partitioned into caps of size \(q-\sqrt q+1\). Under the lifting Singer cycle quadric Veronesians can be glued together to form larger caps of \(PG(5,q)\). For example, it is constructed a complete cap of size 155 in \(PG(5,5)\), a complete cap of size 285 in \(PG(5,7)\), complete caps of size 365 and 438 in \(PG(5,8)\) and a complete cap of size 126 in \(PG(5,4)\).
scientific article; zbMATH DE number 1369767