A Docker image named s390x/alpine is available at Docker Hub and while being a fully functional base, it is just 5 MB (!) in size:
root@s8345001:~# docker run -ti s390x/alpine:3.6The minimal size makes the entire user experience very snappy -- it's fun to work with it.
Unable to find image 's390x/alpine:3.6' locally
3.6: Pulling from s390x/alpine
Status: Downloaded newer image for s390x/alpine:3.6
/ # apk update && apk add curl
OK: 8175 distinct packages available
(1/4) Installing ca-certificates (20161130-r2)
(2/4) Installing libssh2 (1.8.0-r1)
(3/4) Installing libcurl (7.54.0-r0)
(4/4) Installing curl (7.54.0-r0)
OK: 6 MiB in 15 packages
/ # curl containerz.blogspot.com
Few specific tools are missing at this time, so booting Alpine is not yet included: to date, Docker is best way to test drive Alpine.
Credits for this image to Bobby Bingham (musl port to s390x), Tuan Hoang (port of Alpine to s390x, starting from scratch), as well as the core Alpine/Docker folks who provide Alpine itself and put it on Docker Hub/Store.