%0 Journal Article %T Super-simple (v, 4, 2) directed designs and a lower bound for the minimum size of their defining set %A M. Boostan %A S. Golalizadeh %A N. Soltankhah %J Mathematics %D 2015 %I arXiv %X In this paper, we show that for all v\pmod 1 (mod 3), there exists a super- simple (v, 4, 2) directed design. Also, we show that for these parameters there exists a super-simple (v, 4, 2) directed design whose each defining set has at least a half of the blocks. %U http://arxiv.org/abs/1508.00098v1