Estimating the average, variance, and central scaled moments up to the, 4, for the number of occurences of the number of ONES in row-echelon matric\ es of dimension k by , 2 k, matrices over GF(q) with q=, 3 for k from, 50, to , 60 by simulating, 1000, times using the amazing Calabi-Wilf algorithm for random\ ly 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 simulation, each of them, 1000, times, three times to check that it is reliable For , 50, by , 100, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [883.3580000, 548.9322, .1657241967, 2.974362172] [883.8790000, 599.7066, -.1403916382e-1, 2.682806600] [882.6910000, 587.2655, -.6113209332e-1, 3.083730837] The exact values are [883.0168556, 555.5742190, 0.01415409691, 2.999399936] For , 51, by , 102, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [919.0190000, 616.0304, .4992151097e-1, 2.943934350] [919.0570000, 583.0702, -.4759401974e-1, 3.097520161] [917.5800000, 606.5874, -.3226568117e-1, 2.898058743] The exact values are [917.6835223, 578.0186634, 0.01387611026, 2.999423240] For , 52, by , 104, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [953.7530000, 564.2340, .1769821505e-1, 2.979696312] [953.1030000, 632.0266, -.5728431243e-2, 2.773262599] [953.2050000, 628.6770, .1570954670e-1, 2.853166330] The exact values are [953.0168556, 600.9075523, 0.01360884091, 2.999445211] For , 53, by , 106, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [988.7160000, 605.6077, -.5963602069e-2, 2.735585327] [987.2480000, 652.6285, -.1461282882, 3.124512655] [988.2250000, 636.2506, .1183361203, 3.182180768] The exact values are [989.0168556, 624.2408856, 0.01335168037, 2.999465951] For , 54, by , 108, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [1026.278000, 652.376, -.7945087880e-1, 2.751162868] [1026.483000, 622.139, .8534811509e-1, 2.738881232] [1023.288000, 639.513, -.6273719140e-2, 2.976587819] The exact values are [1025.683522, 648.0186634, 0.01310406535, 2.999485550] For , 55, by , 110, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [1062.260000, 705.187, -.6292897542e-1, 2.682890833] [1063.118000, 623.154, -.6817625695e-1, 3.226148925] [1062.889000, 659.804, -.6187027594e-1, 2.766697254] The exact values are [1063.016856, 672.2408856, 0.01286547370, 2.999504088] For , 56, by , 112, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [1101.774000, 703.629, .6825198861e-1, 2.946711293] [1101.262000, 759.600, .3691383079e-1, 2.856676940] [1100.909000, 715.266, -.3460693820e-2, 2.837627830] The exact values are [1101.016856, 696.9075523, 0.01263542070, 2.999521643] For , 57, by , 114, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [1139.214000, 747.572, -.2535639005e-1, 2.896345645] [1139.282000, 707.157, -.8217434051e-2, 3.122144720] [1140.048000, 802.513, .2368862492e-1, 2.831248171] The exact values are [1139.683522, 722.0186634, 0.01241345575, 2.999538282] For , 58, by , 116, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [1179.787000, 699.531, -.3391081439e-1, 3.393410385] [1178.457000, 718.300, -.9007724361e-1, 2.958962360] [1179.262000, 712.658, .1161495321e-1, 2.678766212] The exact values are [1179.016856, 747.5742190, 0.01219915941, 2.999554067] For , 59, by , 118, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [1218.864000, 719.327, -.1130068581e-1, 2.960368257] [1218.351000, 755.014, .1422164601e-1, 2.646214039] [1219.989000, 754.513, -.6014210215e-1, 2.830234093] The exact values are [1219.016856, 773.5742190, 0.01199214081, 2.999569056] For , 60, by , 120, row-echelon matrices over GF(q) with q=, 3, the average,\ variance, and central scaled moments are estimated as follows, doing it\ three times [1259.160000, 818.591, .5848549274e-1, 3.076024671] [1259.251000, 901.240, .6626005245e-1, 3.038317878] [1259.616000, 835.102, -.2033198070, 2.742168718] The exact values are [1259.683522, 800.0186634, 0.01179203517, 2.999583302] ------------------------------------------------------ This ends this article that took, 1254.047, to generate