  In this paper, we establish a second main theorem for holomorphic maps with
finite growth index on complex discs intersecting arbitrary families of
hypersurfaces (fixed and moving) in projective varieties, which gives an above
bound of the sum of truncated defects. Our result also is generalizes and
improves many previous second main theorems for holomorphic maps from $\mathbb
C$ intersecting hypersurfaces (moving and fixed) in projective varieties.
