The embedding in of -geometries with no planar nets

This paper is part of the classification of ( 0 , α ) -geometries ( α > 1 ) embedded in AG ( n , q ) . We study ( 0 , 2 ) -geometries of order ( 2 h - 1 , t ) embedded in AG ( 3 , 2 h ) such that there are no planar nets. In the case t ≠ 2 h , we prove some severe combinatorial restrictions. In the case t = 2 h we provide a classification.