102 RANDOM NUMBERS 3.3.4 Table 1 SAMPLE RESULTS (Best web hosting site)
102 RANDOM NUMBERS 3.3.4 Table 1 SAMPLE RESULTS OF THE SPECTRAL TEST ht a m - 1 23 1OS + 530 530 530 530 447 2 27 + 1 235 16642 16642 16642 15602 252 3 2 8 + 1 235 34359738368 6 4 4 4 4 3141592653 235 2997222016 1026050 27822 1118 1118 5 137 256 274 30 14 6 4 6 3141592621 10 0 4577114792 1034718 62454 1776 542 7 3141592221 10 0 4293881050 276266 97450 3366 2382 8 4219755981 10 0 10721093248 2595578 49362 5868 820 9 4160984121 1010 9183801602 4615650 16686 6840 1344 10 3141592221 235 13539813818 5795090 88134 12716 2938 11 2718281829 235 12939188896 2723830 146116 10782 2914 12 513 235 i3161885770 2925242 113374 13070 2256 13 515 235 32078865098 10274746 167558 5844 2592 14 23+ 212 + 5 235 167510120 8052254 21476 16802 1630 15 23+2l3 + 5 235 168231328 5335322 21476 2008 1134 16 23 +214 + 5 235 12256151168 5733878 21476 13316 2032 17 22 + 213 + 5 235 8201443840 1830230 21476 7786 3080 18 24+ 213 + 5 235 8364058 8364058 21476 16712 1496 19 1993538883: 7 235 32300850938 705518 22270 9558 2660 20 1175245817 235 $6436418002 7362242 95306 3006 2860 21 17059465 235 ~9341117000 9476606 202796 18758 2382 22 216+3 229 536805386 118 116 116 116 23 1812433253 232 4326934538 1462856 15082 4866 906 24 1566083941 232 4659748970 2079590 44902 4652 662 25 69069 232 4243209856 2072544 52804 6990 242 26 1664525 232 4938916874 2322494 63712 4092 1038 27 314159269 2131 -1432232969 899290 36985 3427 1144 ^_ ^ _^ 28 see I:39: I (2;J -1) 1.4 X 10 643578623 12930027 837632 29 31167285 249 3.2 X 1014 4111841446 17341510 306326 59278 30 see the text 294 8.8 x lo18 6.4 x 1012 4.1 x 10 45662836 1846368 :I Thus, in six or fewer dimensions the merit is computed as follows: We might say that the multiplier a passes the spectral test if pt is 0.1 or more for 2 < t 5 6, and it passes with flying colors if pt > 1 for all these t. A low value of pt means that we have probably picked a very unfortunate multiplier, since very few lattices will have integer points so close to the origin. Conversely, a high value of /.~t means that we have found an unusually good multiplier for the given m; but it does not mean that the random numbers are necessarily very good, since m might be too small. Only the values vt truly indicate the degree of randomness.