ts,a_8,$ $b_1,\ldots,b_8$ and computing the coefficients $c(\alpha)$ defined in Sec. II. More precisely, for each example we write all probabilities entering the sums $S_1$, $S_2$, $S_3$ as the marginals of joint probability distribution. As a result we obtain the expressions of the form $$S=\sum_\alpha c(\alpha)p(\alpha)$$ where $\alpha$ runs over all $3^{16}$ configurations of the variables $a_1,\ldots,a_8,b_1,\ldots,b_8$. The results of numerical computations are summarized in the Table below.

  ------------- ----------------------- ------------- ----------------------- ------------- -----------------------
  $c(\alpha)$     No. of configurations $c(\alpha)$     No. of configurations $c(\alpha)$     No. of configurations
  1                              12 960 1                               9 720 1                              18 360
  2                             159 408 2                             126 576 2                             115 596
  3                             645 408 3                             510 480 3                             474 696
  4                           1 729 188 4                           1 514 862 4                           1 445 778
  5                           3 479 760 5                           3 182 904 5                           3 286 224
  6                           5 424 408 6                            5 374584 6                           5 510 160
  7                           6 896 016 7                           7 139 664 7                           7 178 976
  8                           7 261 569 8                           7 822 791 8                           7 670 547
  9                           6 410 016 9                           6 903 648 9                           6 795 936
  10                          4 866 480 10                          5 058 216 10                          5 012 208
  11                          3 176 496 11                          3 006 000 11                          3 087 504
  12                          1 758 3