diff --git a/setup.py b/setup.py
index 2644c03b1637..8cb0d7bbbd68 100644
--- a/setup.py
+++ b/setup.py
@@ -47,12 +47,6 @@ def get_nvcc_cuda_version(cuda_dir: str) -> Version:
         raise RuntimeError(
             "GPUs with compute capability less than 7.0 are not supported.")
     compute_capabilities.add(major * 10 + minor)
-# If no GPU is available, add all supported compute capabilities.
-if not compute_capabilities:
-    compute_capabilities = {70, 75, 80, 86, 90}
-# Add target compute capabilities to NVCC flags.
-for capability in compute_capabilities:
-    NVCC_FLAGS += ["-gencode", f"arch=compute_{capability},code=sm_{capability}"]
 
 # Validate the NVCC CUDA version.
 nvcc_cuda_version = get_nvcc_cuda_version(CUDA_HOME)
@@ -65,6 +59,18 @@ def get_nvcc_cuda_version(cuda_dir: str) -> Version:
     raise RuntimeError(
         "CUDA 11.8 or higher is required for GPUs with compute capability 9.0.")
 
+# If no GPU is available, add all supported compute capabilities.
+if not compute_capabilities:
+    compute_capabilities = {70, 75, 80}
+    if nvcc_cuda_version >= Version("11.1"):
+        compute_capabilities.add(86)
+    if nvcc_cuda_version >= Version("11.8"):
+        compute_capabilities.add(90)
+
+# Add target compute capabilities to NVCC flags.
+for capability in compute_capabilities:
+    NVCC_FLAGS += ["-gencode", f"arch=compute_{capability},code=sm_{capability}"]
+
 # Use NVCC threads to parallelize the build.
 if nvcc_cuda_version >= Version("11.2"):
     num_threads = min(os.cpu_count(), 8)