> MyLLL(L); "Current log2(G.S. lengths):", 33.22, 33.45 "Current log2(G.S. lengths):", 33.22, 33.45, 1.118 "Current log2(G.S. lengths):", 33.22, 28.06 "Current log2(G.S. lengths):", 31.84, 29.44 "Current log2(G.S. lengths):", 30.64, 30.64 "Current log2(G.S. lengths):", 30.64, 30.64, 6.505 "Current log2(G.S. lengths):", 30.64, 29.64 "Current log2(G.S. lengths):", 30.02, 30.25 "Current log2(G.S. lengths):", 30.02, 30.25, 7.515 "Current log2(G.S. lengths):", 30.02, 26.76 "Current log2(G.S. lengths):", 27.24, 29.54 "Current log2(G.S. lengths):", 27.24, 29.54, 11.01 "Current log2(G.S. lengths):", 27.24, 26.90 "Current log2(G.S. lengths):", 27.12, 27.02 "Current log2(G.S. lengths):", 27.12, 27.02, 13.65 "Current log2(G.S. lengths):", 27.12, 24.54 "Current log2(G.S. lengths):", 25.73, 25.92 "Current log2(G.S. lengths):", 25.73, 25.92, 16.13 "Current log2(G.S. lengths):", 25.73, 24.38 "Current log2(G.S. lengths):", 24.60, 25.52 "Current log2(G.S. lengths):", 24.60, 25.52, 17.66 "Current log2(G.S. lengths):", 24.60, 23.82 "Current log2(G.S. lengths):", 24.13, 24.28 "Current log2(G.S. lengths):", 24.13, 24.28, 19.38 "Current log2(G.S. lengths):", 24.13, 22.56 "Current log2(G.S. lengths):", 22.56, 24.13 "Current log2(G.S. lengths):", 22.56, 24.13, 21.10 "Current log2(G.S. lengths):", 22.56, 21.66 "Current log2(G.S. lengths):", 21.85, 22.37 "Current log2(G.S. lengths):", 21.85, 22.37, 23.57 "Current log2(G.S. lengths):", 21.85, 22.37, 23.57, .8320 "Current log2(G.S. lengths):", 21.85, 22.37, 20.81 "Current log2(G.S. lengths):", 21.85, 21.06 "Current log2(G.S. lengths):", 21.06, 21.84 "Current log2(G.S. lengths):", 21.06, 21.84, 22.12 "Current log2(G.S. lengths):", 21.06, 21.84, 22.12, 3.586 "Current log2(G.S. lengths):", 21.06, 21.84, 20.94 "Current log2(G.S. lengths):", 21.06, 20.97 "Current log2(G.S. lengths):", 21.06, 20.97, 21.81 "Current log2(G.S. lengths):", 21.06, 20.97, 21.81, 4.770 "Current log2(G.S. lengths):", 21.06, 20.97, 18.66 "Current log2(G.S. lengths):", 21.06, 19.26 "Current log2(G.S. lengths):", 19.90, 20.42 "Current log2(G.S. lengths):", 19.90, 20.42, 20.37 "Current log2(G.S. lengths):", 19.90, 20.42, 20.37, 7.930 "Current log2(G.S. lengths):", 19.90, 20.42, 19.16 "Current log2(G.S. lengths):", 19.90, 19.40 "Current log2(G.S. lengths):", 19.58, 19.71 "Current log2(G.S. lengths):", 19.58, 19.71, 20.18 "Current log2(G.S. lengths):", 19.58, 19.71, 20.18, 9.135 "Current log2(G.S. lengths):", 19.58, 19.71, 17.91 "Current log2(G.S. lengths):", 19.58, 18.08 "Current log2(G.S. lengths):", 18.64, 19.04 "Current log2(G.S. lengths):", 18.64, 19.04, 19.54 "Current log2(G.S. lengths):", 18.64, 19.04, 19.54, 11.41 "Current log2(G.S. lengths):", 18.64, 19.04, 16.57 "Current log2(G.S. lengths):", 18.64, 18.05 "Current log2(G.S. lengths):", 18.23, 18.46 "Current log2(G.S. lengths):", 18.23, 18.46, 17.56 "Current log2(G.S. lengths):", 18.23, 17.58 "Current log2(G.S. lengths):", 17.64, 18.17 "Current log2(G.S. lengths):", 17.64, 18.17, 18.44 "Current log2(G.S. lengths):", 17.64, 18.17, 18.44, 14.37 "Current log2(G.S. lengths):", 17.64, 18.17, 17.38 "Current log2(G.S. lengths):", 17.64, 17.74 "Current log2(G.S. lengths):", 17.64, 17.74, 17.80 "Current log2(G.S. lengths):", 17.64, 17.74, 17.80, 15.43 "Current log2(G.S. lengths):", 17.64, 17.74, 16.78 "Current log2(G.S. lengths):", 17.64, 17.20 "Current log2(G.S. lengths):", 17.24, 17.61 "Current log2(G.S. lengths):", 17.24, 17.61, 17.33 "Current log2(G.S. lengths):", 17.24, 17.61, 17.33, 16.45 "Current log2(G.S. lengths):", 17.24, 17.61, 16.45 "Current log2(G.S. lengths):", 17.24, 16.52 "Current log2(G.S. lengths):", 16.55, 17.21 "Current log2(G.S. lengths):", 16.55, 17.21, 17.53 "Current log2(G.S. lengths):", 16.55, 17.21, 17.53, 17.33 "Current log2(G.S. lengths):", 16.55, 17.21, 17.53, 17.33, .8310 "Current log2(G.S. lengths):", 16.55, 17.21, 17.53, 15.74 "Current log2(G.S. lengths):", 16.55, 17.21, 16.04 "Current log2(G.S. lengths):", 16.55, 16.06 "Current log2(G.S. lengths):", 16.16, 16.46 "Current log2(G.S. lengths):", 16.16, 16.46, 17.19 "Current log2(G.S. lengths):", 16.16, 16.46, 17.19, 17.22 "Current log2(G.S. lengths):", 16.16, 16.46, 17.19, 17.22, 2.427 "Current log2(G.S. lengths):", 16.16, 16.46, 17.19, 13.88 "Current log2(G.S. lengths):", 16.16, 16.46, 13.95 "Current log2(G.S. lengths):", 16.16, 14.10 "Current log2(G.S. lengths):", 14.46, 15.80 "Current log2(G.S. lengths):", 14.46, 15.80, 16.31 "Current log2(G.S. lengths):", 14.46, 15.80, 16.31, 17.12 "Current log2(G.S. lengths):", 14.46, 15.80, 16.31, 17.12, 5.765 "Current log2(G.S. lengths):", 14.46, 15.80, 16.31, 14.20 "Current log2(G.S. lengths):", 14.46, 15.80, 14.38 "Current log2(G.S. lengths):", 14.46, 14.63 "Current log2(G.S. lengths):", 14.46, 14.63, 15.56 "Current log2(G.S. lengths):", 14.46, 14.63, 15.56, 16.12 "Current log2(G.S. lengths):", 14.46, 14.63, 15.56, 16.12, 8.685 "Current log2(G.S. lengths):", 14.46, 14.63, 15.56, 13.40 "Current log2(G.S. lengths):", 14.46, 14.63, 13.82 "Current log2(G.S. lengths):", 14.46, 13.83 "Current log2(G.S. lengths):", 13.85, 14.44 "Current log2(G.S. lengths):", 13.85, 14.44, 14.62 "Current log2(G.S. lengths):", 13.85, 14.44, 14.62, 15.14 "Current log2(G.S. lengths):", 13.85, 14.44, 14.62, 15.14, 11.41 "Current log2(G.S. lengths):", 13.85, 14.44, 14.62, 13.43 "Current log2(G.S. lengths):", 13.85, 14.44, 13.59 "Current log2(G.S. lengths):", 13.85, 13.69 "Current log2(G.S. lengths):", 13.85, 13.69, 14.34 "Current log2(G.S. lengths):", 13.85, 13.69, 14.34, 14.46 "Current log2(G.S. lengths):", 13.85, 13.69, 14.34, 14.46, 13.12 "Current log2(G.S. lengths):", 13.85, 13.69, 14.34, 13.52 "Current log2(G.S. lengths):", 13.85, 13.69, 13.55 "Current log2(G.S. lengths):", 13.85, 13.69, 13.55, 14.32 "Current log2(G.S. lengths):", 13.85, 13.69, 13.55, 14.32, 14.04 "Current log2(G.S. lengths):", 13.85, 13.69, 13.55, 14.20 "Current log2(G.S. lengths):", 13.85, 13.69, 13.55, 14.20, 14.16 "Current log2(G.S. lengths):", 13.85, 13.69, 13.55, 14.20, 14.16, .7575 "Current log2(G.S. lengths):", 13.85, 13.69, 13.55, 14.20, 8.450 "Current log2(G.S. lengths):", 13.85, 13.69, 13.55, 12.55 "Current log2(G.S. lengths):", 13.85, 13.69, 12.98 "Current log2(G.S. lengths):", 13.85, 12.99 "Current log2(G.S. lengths):", 13.22, 13.62 "Current log2(G.S. lengths):", 13.22, 13.62, 13.68 "Current log2(G.S. lengths):", 13.22, 13.62, 13.68, 13.12 "Current log2(G.S. lengths):", 13.22, 13.62, 13.42 "Current log2(G.S. lengths):", 13.22, 13.50 "Current log2(G.S. lengths):", 13.22, 13.50, 13.54 "Current log2(G.S. lengths):", 13.22, 13.50, 13.54, 13.38 "Current log2(G.S. lengths):", 13.22, 13.50, 13.43 "Current log2(G.S. lengths):", 13.22, 13.50, 13.43, 13.48 "Current log2(G.S. lengths):", 13.22, 13.50, 13.43, 13.48, 10.08 "Current log2(G.S. lengths):", 13.22, 13.50, 13.43, 11.98 "Current log2(G.S. lengths):", 13.22, 13.50, 12.51 "Current log2(G.S. lengths):", 13.22, 12.62 "Current log2(G.S. lengths):", 12.78, 13.06 "Current log2(G.S. lengths):", 12.78, 13.06, 13.39 "Current log2(G.S. lengths):", 12.78, 13.06, 13.39, 12.90 "Current log2(G.S. lengths):", 12.78, 13.06, 12.90 "Current log2(G.S. lengths):", 12.78, 13.06, 12.90, 13.38 "Current log2(G.S. lengths):", 12.78, 13.06, 12.90, 13.38, 11.60 "Current log2(G.S. lengths):", 12.78, 13.06, 12.90, 11.98 "Current log2(G.S. lengths):", 12.78, 13.06, 12.10 "Current log2(G.S. lengths):", 12.78, 12.24 "Current log2(G.S. lengths):", 12.44, 12.58 "Current log2(G.S. lengths):", 12.44, 12.58, 12.92 "Current log2(G.S. lengths):", 12.44, 12.58, 12.92, 12.79 "Current log2(G.S. lengths):", 12.44, 12.58, 12.92, 12.79, 13.00 "Current log2(G.S. lengths):", 12.44, 12.58, 12.92, 12.79, 13.00, 6.475 "Current log2(G.S. lengths):", 12.44, 12.58, 12.92, 12.79, 11.90 "Current log2(G.S. lengths):", 12.44, 12.58, 12.92, 11.90 "Current log2(G.S. lengths):", 12.44, 12.58, 12.34 "Current log2(G.S. lengths):", 12.44, 12.48 "Current log2(G.S. lengths):", 12.44, 12.48, 12.44 "Current log2(G.S. lengths):", 12.44, 12.48, 12.44, 12.48 "Current log2(G.S. lengths):", 12.44, 12.48, 12.44, 12.48, 12.79 "Current log2(G.S. lengths):", 12.44, 12.48, 12.44, 12.48, 12.79, 7.580 "Current log2(G.S. lengths):", 12.44, 12.48, 12.44, 12.48, 11.66 "Current log2(G.S. lengths):", 12.44, 12.48, 12.44, 11.66 "Current log2(G.S. lengths):", 12.44, 12.48, 11.90 "Current log2(G.S. lengths):", 12.44, 12.09 "Current log2(G.S. lengths):", 12.30, 12.23 "Current log2(G.S. lengths):", 12.30, 12.23, 12.28 "Current log2(G.S. lengths):", 12.30, 12.23, 12.28, 12.22 "Current log2(G.S. lengths):", 12.30, 12.23, 12.28, 12.22, 12.48 "Current log2(G.S. lengths):", 12.30, 12.23, 12.28, 12.22, 12.48, 8.705 "Current log2(G.S. lengths):", 12.30, 12.23, 12.28, 12.22, 11.42 "Current log2(G.S. lengths):", 12.30, 12.23, 12.28, 11.65 "Current log2(G.S. lengths):", 12.30, 12.23, 11.68 "Current log2(G.S. lengths):", 12.30, 11.94 "Current log2(G.S. lengths):", 12.04, 12.19 "Current log2(G.S. lengths):", 12.04, 12.19, 11.98 "Current log2(G.S. lengths):", 12.04, 12.08 "Current log2(G.S. lengths):", 12.04, 12.08, 12.08 "Current log2(G.S. lengths):", 12.04, 12.08, 12.08, 12.26 "Current log2(G.S. lengths):", 12.04, 12.08, 12.08, 12.26, 11.99 "Current log2(G.S. lengths):", 12.04, 12.08, 12.08, 12.06 "Current log2(G.S. lengths):", 12.04, 12.08, 12.08, 12.06, 12.18 "Current log2(G.S. lengths):", 12.04, 12.08, 12.08, 12.06, 12.18, 9.755 "Current log2(G.S. lengths):", 12.04, 12.08, 12.08, 12.06, 10.95 "Current log2(G.S. lengths):", 12.04, 12.08, 12.08, 11.24 "Current log2(G.S. lengths):", 12.04, 12.08, 11.35 "Current log2(G.S. lengths):", 12.04, 11.58 "Current log2(G.S. lengths):", 11.72, 11.92 "Current log2(G.S. lengths):", 11.72, 11.92, 11.84 "Current log2(G.S. lengths):", 11.72, 11.92, 11.84, 11.97 "Current log2(G.S. lengths):", 11.72, 11.92, 11.84, 11.97, 11.78 "Current log2(G.S. lengths):", 11.72, 11.92, 11.84, 11.78 "Current log2(G.S. lengths):", 11.72, 11.92, 11.84, 11.78, 11.97 "Current log2(G.S. lengths):", 11.72, 11.92, 11.84, 11.78, 11.97, 10.98 "Current log2(G.S. lengths):", 11.72, 11.92, 11.84, 11.78, 11.26 "Current log2(G.S. lengths):", 11.72, 11.92, 11.84, 11.26 "Current log2(G.S. lengths):", 11.72, 11.92, 11.48 "Current log2(G.S. lengths):", 11.72, 11.48 "Current log2(G.S. lengths):", 11.48, 11.72 "Current log2(G.S. lengths):", 11.48, 11.72, 11.91 "Current log2(G.S. lengths):", 11.48, 11.72, 11.91, 11.62 "Current log2(G.S. lengths):", 11.48, 11.72, 11.62 "Current log2(G.S. lengths):", 11.48, 11.72, 11.62, 11.91 "Current log2(G.S. lengths):", 11.48, 11.72, 11.62, 11.91, 11.76 "Current log2(G.S. lengths):", 11.48, 11.72, 11.62, 11.91, 11.76, 11.70 "Current log2(G.S. lengths):", 11.48, 11.72, 11.62, 11.91, 11.76, 11.70, .7345 "Current log2(G.S. lengths):", 11.48, 11.72, 11.62, 11.91, 11.76, 8.635 "Current log2(G.S. lengths):", 11.48, 11.72, 11.62, 11.91, 9.860 "Current log2(G.S. lengths):", 11.48, 11.72, 11.62, 9.905 "Current log2(G.S. lengths):", 11.48, 11.72, 10.49 "Current log2(G.S. lengths):", 11.48, 10.92 "Current log2(G.S. lengths):", 10.94, 11.48 "Current log2(G.S. lengths):", 10.94, 11.48, 11.28 "Current log2(G.S. lengths):", 10.94, 11.28 "Current log2(G.S. lengths):", 10.94, 11.28, 11.47 "Current log2(G.S. lengths):", 10.94, 11.28, 11.47, 11.04 "Current log2(G.S. lengths):", 10.94, 11.28, 11.27 "Current log2(G.S. lengths):", 10.94, 11.28, 11.27, 11.24 "Current log2(G.S. lengths):", 10.94, 11.28, 11.27, 11.24, 11.86 "Current log2(G.S. lengths):", 10.94, 11.28, 11.27, 11.24, 11.86, 10.54 "Current log2(G.S. lengths):", 10.94, 11.28, 11.27, 11.24, 10.54 "Current log2(G.S. lengths):", 10.94, 11.28, 11.27, 10.59 "Current log2(G.S. lengths):", 10.94, 11.28, 10.94 "Current log2(G.S. lengths):", 10.94, 11.01 "Current log2(G.S. lengths):", 10.94, 11.01, 11.22 "Current log2(G.S. lengths):", 10.94, 11.01, 11.22, 10.92 "Current log2(G.S. lengths):", 10.94, 11.01, 11.22, 10.92, 11.20 "Current log2(G.S. lengths):", 10.94, 11.01, 11.22, 10.92, 11.20, 11.86 "Current log2(G.S. lengths):", 10.94, 11.01, 11.22, 10.92, 11.20, 11.86, 3.803 "Current log2(G.S. lengths):", 10.94, 11.01, 11.22, 10.92, 11.20, 10.54 "Current log2(G.S. lengths):", 10.94, 11.01, 11.22, 10.92, 10.62 "Current log2(G.S. lengths):", 10.94, 11.01, 11.22, 10.62 "Current log2(G.S. lengths):", 10.94, 11.01, 10.90 "Current log2(G.S. lengths):", 10.94, 11.01, 10.90, 10.95 "Current log2(G.S. lengths):", 10.94, 11.01, 10.90, 10.95, 10.92 "Current log2(G.S. lengths):", 10.94, 11.01, 10.90, 10.95, 10.92, 11.12 "Current log2(G.S. lengths):", 10.94, 11.01, 10.90, 10.95, 10.92, 11.12, 5.125 "Current log2(G.S. lengths):", 10.94, 11.01, 10.90, 10.95, 10.92, 10.10 "Current log2(G.S. lengths):", 10.94, 11.01, 10.90, 10.95, 10.35 "Current log2(G.S. lengths):", 10.94, 11.01, 10.90, 10.54 "Current log2(G.S. lengths):", 10.94, 11.01, 10.54 "Current log2(G.S. lengths):", 10.94, 10.54 "Current log2(G.S. lengths):", 10.64, 10.84 "Current log2(G.S. lengths):", 10.64, 10.84, 11.00 "Current log2(G.S. lengths):", 10.64, 10.84, 11.00, 10.90 "Current log2(G.S. lengths):", 10.64, 10.84, 11.00, 10.90, 10.76 "Current log2(G.S. lengths):", 10.64, 10.84, 11.00, 10.90, 10.76, 10.66 "Current log2(G.S. lengths):", 10.64, 10.84, 11.00, 10.90, 10.76, 10.66, 6.140 "Current log2(G.S. lengths):", 10.64, 10.84, 11.00, 10.90, 10.76, 6.250 "Current log2(G.S. lengths):", 10.64, 10.84, 11.00, 10.90, 6.255 "Current log2(G.S. lengths):", 10.64, 10.84, 11.00, 6.345 "Current log2(G.S. lengths):", 10.64, 10.84, 6.415 "Current log2(G.S. lengths):", 10.64, 6.520 "Current log2(G.S. lengths):", 6.635, 10.52 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.94 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.94, 10.80 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.92 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.92, 10.76 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.82 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.82, 10.87 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.82, 10.87, 10.54 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.82, 10.61 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.68 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.68, 10.74 "Current log2(G.S. lengths):", 6.635, 10.52, 10.74, 10.82, 10.68, 10.74, 10.80 [[-7, 8, 47, -45, 45, -6, 42, -35, -22], [845, -100, 344, -431, -418, -388, -269, -481, 720], [-83, -850, -387, -380, 819, 452, 438, 1012, 327], [-100, 229, -1129, -1145, -611, -20, 303, -480, 342], [-399, 701, -582, 39, 613, 754, 711, 105, 1079], [-1057, -259, 695, 442, -23, -541, -235, -464, 1081], [-241, 1039, 499, -602, -519, -565, 208, 888, 962]] Observe that the original log2(G.S. lengths) were: 33.22, 33.45, 1.118, 0.8320, 0.8310, 0.7575, 0.7345 while the final log2(G.S. lengths) were: 6.635, 10.52, 10.74, 10.82, 10.68, 10.74, 10.80 so the earlier ones went down and the later ones went up. Also observe that in each swap, one of them went down (by at least "MinProgress") while the next one went up by the same amount. So each swap gradually moved some log2(Gram-Schmidt length) from a vector to the next. The result of all of that is two-fold: 1) We no longer have a tiny G.S. length like 0.7345 (again, this is on a log2-scale). This means that the lower bound for the shortest vector is no longer a bad bound. 2) The first G.S. vector went down a lot, from 33.22 to 6.635 on a log2-scale. That's good because the first G.S. vector is also an actual vector (an element of our lattice) (the same is generally not true for the other G.S. vectors). Moving G.S. length towards later vectors caused the first G.S. vector to become small, but that led to a small actual vector.