diff --git a/qrcode/main.py b/qrcode/main.py
index 593c581b..ace23ca4 100644
--- a/qrcode/main.py
+++ b/qrcode/main.py
@@ -219,12 +219,16 @@ def best_fit(self, start=None):
             data.write(buffer)
 
         needed_bits = len(buffer)
-        # Create a thread-local copy of the table to avoid concurrent access issues (Python 3.13+)
-        self.version = bisect_left(
+        # Compute the version from a thread-local view of the limit table.
+        # Bisect first, then check overflow, *before* assigning to the setter
+        # so we raise the semantically correct DataOverflowError instead of
+        # the ValueError the version setter would raise for value 41.
+        new_version = bisect_left(
             util.BIT_LIMIT_TABLE[self.error_correction][:], needed_bits, start
         )
-        if self.version == 41:
+        if new_version == 41:
             raise exceptions.DataOverflowError
+        self.version = new_version
 
         # Now check whether we need more bits for the mode sizes, recursing if
         # our guess was too low
diff --git a/qrcode/util.py b/qrcode/util.py
index 4187aa5e..ea73e44c 100644
--- a/qrcode/util.py
+++ b/qrcode/util.py
@@ -158,7 +158,7 @@ def mask_func(pattern):
         return lambda i, j: ((i * j) % 2 + (i * j) % 3) % 2 == 0
     if pattern == 7:  # 111
         return lambda i, j: ((i * j) % 3 + (i + j) % 2) % 2 == 0
-    raise TypeError("Bad mask pattern: " + pattern)  # pragma: no cover
+    raise ValueError(f"Bad mask pattern: {pattern!r}")
 
 
 def mode_sizes_for_version(version):
@@ -456,11 +456,22 @@ def write(self, buffer):
             for i in range(0, len(self.data), 2):
                 chars = self.data[i : i + 2]
                 if len(chars) > 1:
-                    buffer.put(
-                        ALPHA_NUM.find(chars[0]) * 45 + ALPHA_NUM.find(chars[1]), 11
-                    )
+                    a = ALPHA_NUM.find(chars[0])
+                    b = ALPHA_NUM.find(chars[1])
+                    if a < 0 or b < 0:
+                        raise ValueError(
+                            f"Character {chars!r} is not in the alphanumeric "
+                            f"table; cannot encode in MODE_ALPHA_NUM"
+                        )
+                    buffer.put(a * 45 + b, 11)
                 else:
-                    buffer.put(ALPHA_NUM.find(chars), 6)
+                    a = ALPHA_NUM.find(chars)
+                    if a < 0:
+                        raise ValueError(
+                            f"Character {chars!r} is not in the alphanumeric "
+                            f"table; cannot encode in MODE_ALPHA_NUM"
+                        )
+                    buffer.put(a, 6)
         else:
             # Iterating a bytestring in Python 3 returns an integer,
             # no need to ord().