[Design of experiments and algebraic cycles].
It is well-known that balanced incomplete block designs are closely connected with finite geometry. A block design can be obtained by identifying rational points of an algebraic variety with treatments. The number of GF(qs)-rational points follows from the theory of étale cohomologies. It is, however, difficult to give an explicit formula for the number. We shall discuss the number of the GF(qs)-rational points of the variety of non-isotropic subspaces.
D008433:Mathematics; D012107:Research Design