ipod touch 5: Lightning plug to 1/8" male, line out/in, audio plug /cable

I have an ipod touch 5th generation with a 16 pin lightning plug. I use the headphone out (1/8" male phono plug to rca plug adapter) to feed audio to my home stereo... I would rather use a "line out" feed from my ipod lightning plug (I attached a 32 pin adapter plug and connected my iopd to an iDeck ((car cassette adapter)) and, yes, there is a line out feed)- a line out feed would eliminate internal ipod amplification and inherent distortion. I can't find a 16 pin male adapter (ipod input) to 1/8" stereo phono plug cable!? Is there such an animal