International Centre for Theoretical Physics a New Basis for Trades International Atomic Energy Agency United Nations Educational, Scientific and Cultural Organization

A very fast algorithm to generate a semitriangular basis for trades consisting of minimal trades (sparsest basis) is given. By augmenting the elements of this basis, we construct an infinite family of 2-designs. MIRAMARE TRIESTE August 1988 To be submitted for publication. This research was supported in part by a grant from the Research Council of the University of Tehran and was completed while G.B. Khosrovshahi was visiting ICTP. Permanent address: Department of Mathematics and Computer Science, University of Tehran and Centre for Theoretical Physics and Mathematics (AEOI), Tehran, Iran.