Small sample uniformity in random number generation

Nonstatistical notions of uniformity suitable for small samples are proposed and studied. New algorithms are presented for generation of small samples of quasi-random points good with respect to distance, plane projection, or plane section uniformity. Examples are presented for visual evaluation of uniformity in small samples on the screen of computers. The methods can be used for generation of quasi-random lattices for nonconvex global optimization, multiple integration, and other applications.