gh-38973: is_t_design needs to verify that every t-tuple is in at least one block
    
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Fixes #38454.

In a t-design, every t-tuple needs to be contained in the same number of
blocks. The code for `is_t_design` did not verify this correctly,
because it only checked the t-tuples that are contained in at least one
block. We fix this by verifying that the number of t-tuples that appear
in at least one block is equal to the total number of t-tuples.

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URL: #38973
Reported by: DaveWitteMorris
Reviewer(s): David Coudert

Author: Release Manager

src/sage/combinat/designs/incidence_structures.py

@@ -1592,6 +1592,13 @@ def is_t_design(self, t=None, v=None, k=None, l=None, return_parameters=False):
             sage: I = IncidenceStructure(2, [[0],[0,1]])
             sage: I.is_t_design(return_parameters=True)
             (False, (0, 0, 0, 0))
+
+        Verify that :issue:`38454` is fixed::
+
+            sage: I = IncidenceStructure(points=[0,1,2,3,4,5],
+            ....:                        blocks=[[0,1], [1,2], [0,2]])
+            sage: I.is_t_design(return_parameters=True)
+            (True, (0, 6, 2, 3))
         """
         from sage.arith.misc import binomial
 
@@ -1653,7 +1660,7 @@ def is_t_design(self, t=None, v=None, k=None, l=None, return_parameters=False):
                 for i in combinations(block, tt):
                     s[i] = s.get(i, 0) + 1
 
-            if len(set(s.values())) != 1:
+            if (len(s) != binomial(v, tt)) or (len(set(s.values())) != 1):
                 tt -= 1
                 break