Standard shader issue with generated mesh

Even though I looked in many places in the forum on this known issue, I was not able to fix it. I am posting my code here to check if somebody can find what is wrong.

I am generating a mesh for a cylinder from scratch in the code directly, but the standard shader still displays flat faces for the mesh.

     public int nbase = 15;
     public int nspan = 10;
 
     private Mesh mesh;
     void Start () {
         MeshFilter meshFilter = gameObject.GetComponent<MeshFilter>();
         mesh = new Mesh();
         mesh.name = "cylinder";
         meshFilter.sharedMesh = mesh;
         mesh.Clear();        
         mesh.vertices = getVertices();
         mesh.triangles = getTriangles();
         mesh.RecalculateNormals();
         mesh.RecalculateBounds();
         mesh.Optimize();
     }
 
     Vector3[] getVertices() {
         Vector3[] vertices = new Vector3[(int)(nspan * nbase)];
         int index = 0;
         for (int j = 0; j < nspan; j++)
         {
             for (int i = 0; i < nbase; i++)
             {
                 float a = (float)i * 2f * Mathf.PI / nbase;
                 vertices[index] = 0.5f * (new Vector3(Mathf.Cos(a), (float)j, Mathf.Sin(a)));
                 index++;
             }
         }
         return vertices;
     }
 
     int[] getTriangles() {
         int[] myTriangles = new int[(int)(3f * 2f * ((float)nspan - 1f) * ((float)nbase - 1f))];
         int index = 0;
         for (int j = 0; j < nspan - 1; j++)
         {
             for (int i = 0; i < nbase - 1; i++)
             {
                 myTriangles[index] = i + (int)((float)j * (float)nbase);
                 myTriangles[index + 1] = i + (int)((float)(j + 1) * (float)nbase);
                 myTriangles[index + 2] = i + 1 + (int)((float)j * (float)nbase);
                 myTriangles[index + 3] = i + 1 + (int)((float)j * (float)nbase);
                 myTriangles[index + 4] = i + (int)((float)(j + 1) * (float)nbase);
                 myTriangles[index + 5] = i + 1 + (int)((float)(j + 1) * (float)nbase);
                 index += 6;
             }
         }
 
         return myTriangles;
     }

Here is a picture of the result. I used the MeshDisplay script to represent my normals in the editor. I tried also to use the NormalSolver from http://schemingdeveloper.com to use alternative method to compute my normals, but it did not change the result.

What I am looking for here is to get my cylinder smooth. Any idea/suggestion would be very welcomed.