Non-existence of a simple 3-(16,7,5) design with an automorphism of order 3

Using recent results concerning tactical decompositions of t-designs with t > 2, we make a step forward on the long-standing question about the existence of a simple 3-(16, 7, 5) design; if such a design exists, then its full automorphism group has order a power of 2, possibly equal to 1. (C) 2014 Elsevier B.V. All rights reserved.