On Ubuntu 18.04, testing various optional and external packages, I get:

Using 
--optional=4ti2,cbc,ccache,cryptominisat,database_jones_numfield,debian,dot2tex,e_antic,external,fricas,glucose,latte_int,libnauty,lidia,lrslib,memlimit,normaliz,notedown,pandoc_attributes,pip,pycosat,pynormaliz,rst2ipynb,sage,sage_numerical_backends_coin,sage_spkg

----------------------------------------------------------------------
sage -t --long --warn-long 72.7 --random-seed=0 
src/sage/databases/findstat.py  # 2 doctests failed
sage -t --long --warn-long 72.7 --random-seed=0 
src/sage/combinat/designs/ext_rep.py  # 1 doctest failed
----------------------------------------------------------------------
External software detected for doctesting: 
ffmpeg,graphviz,imagemagick,internet,latex,octave,pandoc

Rerunning failed tests, I obtain:

----------------------------------------------------------------------
sage -t --long --warn-long 72.1 --random-seed=0 
src/sage/databases/findstat.py  # 2 doctests failed
----------------------------------------------------------------------
External software detected for doctesting: internet

The issue with ext_rep.py which does not reproduce is:

sage -t --long --warn-long 72.7 --random-seed=0 
src/sage/combinat/designs/ext_rep.py
**********************************************************************
File "src/sage/combinat/designs/ext_rep.py", line 1049, in 
sage.combinat.designs.ext_rep.designs_from_XML_url
Failed example:
    
ext_rep.designs_from_XML_url("http://designtheory.org/database/v-b-k/v3-b6-k2.icgsa.txt.bz2";)
 
# optional - internet
Expected:
    [(3, [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 2]]),
     (3, [[0, 1], [0, 1], [0, 1], [0, 1], [0, 2], [0, 2]]),
     (3, [[0, 1], [0, 1], [0, 1], [0, 1], [0, 2], [1, 2]]),
     (3, [[0, 1], [0, 1], [0, 1], [0, 2], [0, 2], [0, 2]]),
     (3, [[0, 1], [0, 1], [0, 1], [0, 2], [0, 2], [1, 2]]),
     (3, [[0, 1], [0, 1], [0, 2], [0, 2], [1, 2], [1, 2]])]
Got:
    []
**********************************************************************
1 item had failures:
   1 of   7 in sage.combinat.designs.ext_rep.designs_from_XML_url
    0 tests not run because we ran out of time
    [102 tests, 1 failure, 17.82 s]

The issue with findstat was already reported. Follow-up at: 
https://trac.sagemath.org/ticket/25536

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