diff --git a/estimator/lwe_primal.py b/estimator/lwe_primal.py
index 277ca35..85c2dd7 100644
--- a/estimator/lwe_primal.py
+++ b/estimator/lwe_primal.py
@@ -303,8 +303,8 @@ def gaussian_heuristic_log_input(r):
 
         if d > 4096:
             for i, _ in enumerate(r):
-                # chosen arbitrarily
-                j = d - 1024 + i
+                # chosen since RC.ADPS16(1754, 1754).log(2.) = 512.168000000000
+                j = d - 1754 + i
                 if gaussian_heuristic_log_input(r[j:]) < D.stddev**2 * (d - j):
                     return ZZ(d - (j - 1))
             return ZZ(2)