Comparing the Estimates of the average number  of ONES in row-echelon matric\

    es of dimension k by , 3 k, matrices over GF(q) with q=, 2

                           for k from, 100,  to , 110

by simulating, 1000, times, using the amazing Calabi-Wilf algorithm for rando\
    mly generating a k-subspace of GF(q)^n

                     and comparing it to the exact values



                              By Shalosh B. Ekhad



Below for the given dimension we repeat the simulations each of them, 1000,  \
    times , and repeating each simulation three times to check that it is re\
    liable

For , 100,  by , 300, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

10101.98200


10097.33800


10097.47400




                        The exact value is , 10098.62798

For , 101,  by , 303, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

10301.60200


10303.62200


10298.32700




                        The exact value is , 10300.62798

For , 102,  by , 306, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

10506.40500


10507.40900


10505.95500




                        The exact value is , 10504.62798

For , 103,  by , 309, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

10711.41000


10712.44800


10709.33200




                        The exact value is , 10710.62798

For , 104,  by , 312, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

10916.73800


10917.15400


10919.33800




                        The exact value is , 10918.62798

For , 105,  by , 315, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

11129.53200


11126.23700


11132.06800




                        The exact value is , 11128.62798

For , 106,  by , 318, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

11339.79100


11338.44200


11339.36300




                        The exact value is , 11340.62798

For , 107,  by , 321, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

11558.95700


11556.28100


11552.48200




                        The exact value is , 11554.62798

For , 108,  by , 324, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

11767.60900


11774.10100


11769.35300




                        The exact value is , 11770.62798

For , 109,  by , 327, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

11987.42100


11990.33400


11990.85900




                        The exact value is , 11988.62798

For , 110,  by , 330, row-echelon matrices over GF(q) with q=, 2,

    the average is  estimated as follows, doing it three times

12207.99200


12210.59400


12204.01000




                        The exact value is , 12208.62798



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            This ends this article that took, 4584.546, to generate