diff --git a/src/sage/combinat/designs/covering_array.py b/src/sage/combinat/designs/covering_array.py
index 75e5ae9b10e..d59c2655aa0 100644
--- a/src/sage/combinat/designs/covering_array.py
+++ b/src/sage/combinat/designs/covering_array.py
@@ -177,6 +177,7 @@ def __init__(self, Array, SymbolSet=None):
         #number of unique entries.
         if SymbolSet is None:
             SymbolSet = list({x for l in Array for x in l})
+            SymbolSet.sort()
         self.__sset=SymbolSet
 
     def numrows(self):
@@ -230,6 +231,9 @@ def symbolset(self):
             sage: CA = CoveringArray(C,GF(2))
             sage: CA.symbolset()
             Finite Field of size 2
+            sage: CA = CoveringArray(C)
+            sage: CA.symbolset()
+            [0, 1]
         """
         return self.__sset
 
@@ -337,6 +341,64 @@ def strength(self):
             sage: CA = CoveringArray(C,GF(2))
             sage: CA.strength()
             2
+
+
+            sage: C2 = ((1, 0, 0, 2, 0, 2, 1, 2, 2, 1, 0, 2, 2),\
+                    (1, 1, 0, 0, 2, 0, 2, 1, 2, 2, 1, 0, 2),\
+                    (1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 2, 1, 0),\
+                    (0, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 2, 1),\
+                    (2, 0, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 2),\
+                    (1, 2, 0, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2),\
+                    (1, 1, 2, 0, 1, 1, 1, 0, 0, 2, 0, 2, 1),\
+                    (2, 1, 1, 2, 0, 1, 1, 1, 0, 0, 2, 0, 2),\
+                    (1, 2, 1, 1, 2, 0, 1, 1, 1, 0, 0, 2, 0),\
+                    (0, 1, 2, 1, 1, 2, 0, 1, 1, 1, 0, 0, 2),\
+                    (1, 0, 1, 2, 1, 1, 2, 0, 1, 1, 1, 0, 0),\
+                    (0, 1, 0, 1, 2, 1, 1, 2, 0, 1, 1, 1, 0),\
+                    (0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 1, 1, 1),\
+                    (2, 0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 1, 1),\
+                    (2, 2, 0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 1),\
+                    (2, 2, 2, 0, 0, 1, 0, 1, 2, 1, 1, 2, 0),\
+                    (0, 2, 2, 2, 0, 0, 1, 0, 1, 2, 1, 1, 2),\
+                    (1, 0, 2, 2, 2, 0, 0, 1, 0, 1, 2, 1, 1),\
+                    (2, 1, 0, 2, 2, 2, 0, 0, 1, 0, 1, 2, 1),\
+                    (2, 2, 1, 0, 2, 2, 2, 0, 0, 1, 0, 1, 2),\
+                    (1, 2, 2, 1, 0, 2, 2, 2, 0, 0, 1, 0, 1),\
+                    (2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 0, 1, 0),\
+                    (0, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 0, 1),\
+                    (2, 0, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 0),\
+                    (0, 2, 0, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0),\
+                    (0, 0, 2, 0, 2, 1, 2, 2, 1, 0, 2, 2, 2),\
+                    (1, 1, 0, 2, 1, 1, 2, 1, 0, 1, 0, 0, 2),\
+                    (1, 1, 1, 0, 2, 1, 1, 2, 1, 0, 1, 0, 0),\
+                    (0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 0, 1, 0),\
+                    (0, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 0, 1),\
+                    (2, 0, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 0),\
+                    (0, 2, 0, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1),\
+                    (2, 0, 2, 0, 0, 1, 1, 1, 0, 2, 1, 1, 2),\
+                    (1, 2, 0, 2, 0, 0, 1, 1, 1, 0, 2, 1, 1),\
+                    (2, 1, 2, 0, 2, 0, 0, 1, 1, 1, 0, 2, 1),\
+                    (2, 2, 1, 2, 0, 2, 0, 0, 1, 1, 1, 0, 2),\
+                    (1, 2, 2, 1, 2, 0, 2, 0, 0, 1, 1, 1, 0),\
+                    (0, 1, 2, 2, 1, 2, 0, 2, 0, 0, 1, 1, 1),\
+                    (2, 0, 1, 2, 2, 1, 2, 0, 2, 0, 0, 1, 1),\
+                    (2, 2, 0, 1, 2, 2, 1, 2, 0, 2, 0, 0, 1),\
+                    (2, 2, 2, 0, 1, 2, 2, 1, 2, 0, 2, 0, 0),\
+                    (0, 2, 2, 2, 0, 1, 2, 2, 1, 2, 0, 2, 0),\
+                    (0, 0, 2, 2, 2, 0, 1, 2, 2, 1, 2, 0, 2),\
+                    (1, 0, 0, 2, 2, 2, 0, 1, 2, 2, 1, 2, 0),\
+                    (0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 2, 1, 2),\
+                    (1, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 2, 1),\
+                    (2, 1, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 2),\
+                    (1, 2, 1, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2),\
+                    (1, 1, 2, 1, 0, 1, 0, 0, 2, 2, 2, 0, 1),\
+                    (2, 1, 1, 2, 1, 0, 1, 0, 0, 2, 2, 2, 0),\
+                    (0, 2, 1, 1, 2, 1, 0, 1, 0, 0, 2, 2, 2),\
+                    (1, 0, 2, 1, 1, 2, 1, 0, 1, 0, 0, 2, 2),\
+                    (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
+            sage: CA2 = CoveringArray(C2,GF(3))
+            sage: CA2.strength()
+            3
         """
         finished=False
         strength=1