self-tests passed
(A) delta>=0: non-excluded (n,k), k>=3, n<=60: [(37, 3), (42, 3), (47, 3), (51, 4), (52, 3), (57, 3), (58, 3), (58, 4)]
(A) delta>=1: non-excluded (n,k), k>=3, n<=60: [(57, 3)]
(B) delta>=0: every (n,k) with n<=36, k>=3 excluded? True  []
(B) delta>=1: every (n,k) with n<=56, k>=3 excluded? True  []
(B') k=2, delta>=0: non-excluded n<=60 (informational; bipartite case handled by Prop 5.1): [23, 26, 29, 32, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]
(C) k= 3: least non-excluded n (delta>=0) = 37 [14k-5=37], (delta>=1) = 57 [22k-9=57]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (19, 16, 109, 13), at 22k-10: (31, 26, 281, 21)
(C) k= 4: least non-excluded n (delta>=0) = 51 [14k-5=51], (delta>=1) = 79 [22k-9=79]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (26, 23, 158, 20), at 22k-10: (42, 37, 402, 32)
(C) k= 5: least non-excluded n (delta>=0) = 65 [14k-5=65], (delta>=1) = 101 [22k-9=101]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (33, 30, 207, 27), at 22k-10: (53, 48, 523, 43)
(C) k= 6: least non-excluded n (delta>=0) = 79 [14k-5=79], (delta>=1) = 123 [22k-9=123]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (40, 37, 256, 34), at 22k-10: (64, 59, 644, 54)
(C) k= 7: least non-excluded n (delta>=0) = 93 [14k-5=93], (delta>=1) = 145 [22k-9=145]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (47, 44, 305, 41), at 22k-10: (75, 70, 765, 65)
(C) k= 8: least non-excluded n (delta>=0) = 107 [14k-5=107], (delta>=1) = 167 [22k-9=167]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (54, 51, 354, 48), at 22k-10: (86, 81, 886, 76)
(C) k= 9: least non-excluded n (delta>=0) = 121 [14k-5=121], (delta>=1) = 189 [22k-9=189]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (61, 58, 403, 55), at 22k-10: (97, 92, 1007, 87)
(C) k=10: least non-excluded n (delta>=0) = 135 [14k-5=135], (delta>=1) = 211 [22k-9=211]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (68, 65, 452, 62), at 22k-10: (108, 103, 1128, 98)
(C) k=11: least non-excluded n (delta>=0) = 149 [14k-5=149], (delta>=1) = 233 [22k-9=233]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (75, 72, 501, 69), at 22k-10: (119, 114, 1249, 109)
(C) k=12: least non-excluded n (delta>=0) = 163 [14k-5=163], (delta>=1) = 255 [22k-9=255]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (82, 79, 550, 76), at 22k-10: (130, 125, 1370, 120)
(C) k=13: least non-excluded n (delta>=0) = 177 [14k-5=177], (delta>=1) = 277 [22k-9=277]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (89, 86, 599, 83), at 22k-10: (141, 136, 1491, 131)
(C) k=14: least non-excluded n (delta>=0) = 191 [14k-5=191], (delta>=1) = 299 [22k-9=299]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (96, 93, 648, 90), at 22k-10: (152, 147, 1612, 142)
(C) k=15: least non-excluded n (delta>=0) = 205 [14k-5=205], (delta>=1) = 321 [22k-9=321]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (103, 100, 697, 97), at 22k-10: (163, 158, 1733, 153)
(C) k=16: least non-excluded n (delta>=0) = 219 [14k-5=219], (delta>=1) = 343 [22k-9=343]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (110, 107, 746, 104), at 22k-10: (174, 169, 1854, 164)
(C) k=17: least non-excluded n (delta>=0) = 233 [14k-5=233], (delta>=1) = 365 [22k-9=365]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (117, 114, 795, 111), at 22k-10: (185, 180, 1975, 175)
(C) k=18: least non-excluded n (delta>=0) = 247 [14k-5=247], (delta>=1) = 387 [22k-9=387]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (124, 121, 844, 118), at 22k-10: (196, 191, 2096, 186)
(C) k=19: least non-excluded n (delta>=0) = 261 [14k-5=261], (delta>=1) = 409 [22k-9=409]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (131, 128, 893, 125), at 22k-10: (207, 202, 2217, 197)
(C) k=20: least non-excluded n (delta>=0) = 275 [14k-5=275], (delta>=1) = 431 [22k-9=431]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (138, 135, 942, 132), at 22k-10: (218, 213, 2338, 208)
(C) k=21: least non-excluded n (delta>=0) = 289 [14k-5=289], (delta>=1) = 453 [22k-9=453]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (145, 142, 991, 139), at 22k-10: (229, 224, 2459, 219)
(C) k=22: least non-excluded n (delta>=0) = 303 [14k-5=303], (delta>=1) = 475 [22k-9=475]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (152, 149, 1040, 146), at 22k-10: (240, 235, 2580, 230)
(C) k=23: least non-excluded n (delta>=0) = 317 [14k-5=317], (delta>=1) = 497 [22k-9=497]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (159, 156, 1089, 153), at 22k-10: (251, 246, 2701, 241)
(C) k=24: least non-excluded n (delta>=0) = 331 [14k-5=331], (delta>=1) = 519 [22k-9=519]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (166, 163, 1138, 160), at 22k-10: (262, 257, 2822, 252)
(C) k=25: least non-excluded n (delta>=0) = 345 [14k-5=345], (delta>=1) = 541 [22k-9=541]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (173, 170, 1187, 167), at 22k-10: (273, 268, 2943, 263)
(C) k=26: least non-excluded n (delta>=0) = 359 [14k-5=359], (delta>=1) = 563 [22k-9=563]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (180, 177, 1236, 174), at 22k-10: (284, 279, 3064, 274)
(C) k=27: least non-excluded n (delta>=0) = 373 [14k-5=373], (delta>=1) = 585 [22k-9=585]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (187, 184, 1285, 181), at 22k-10: (295, 290, 3185, 285)
(C) k=28: least non-excluded n (delta>=0) = 387 [14k-5=387], (delta>=1) = 607 [22k-9=607]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (194, 191, 1334, 188), at 22k-10: (306, 301, 3306, 296)
(C) k=29: least non-excluded n (delta>=0) = 401 [14k-5=401], (delta>=1) = 629 [22k-9=629]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (201, 198, 1383, 195), at 22k-10: (317, 312, 3427, 307)
(C) k=30: least non-excluded n (delta>=0) = 415 [14k-5=415], (delta>=1) = 651 [22k-9=651]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (208, 205, 1432, 202), at 22k-10: (328, 323, 3548, 318)
(C) k=31: least non-excluded n (delta>=0) = 429 [14k-5=429], (delta>=1) = 673 [22k-9=673]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (215, 212, 1481, 209), at 22k-10: (339, 334, 3669, 329)
(C) k=32: least non-excluded n (delta>=0) = 443 [14k-5=443], (delta>=1) = 695 [22k-9=695]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (222, 219, 1530, 216), at 22k-10: (350, 345, 3790, 340)
(C) k=33: least non-excluded n (delta>=0) = 457 [14k-5=457], (delta>=1) = 717 [22k-9=717]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (229, 226, 1579, 223), at 22k-10: (361, 356, 3911, 351)
(C) k=34: least non-excluded n (delta>=0) = 471 [14k-5=471], (delta>=1) = 739 [22k-9=739]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (236, 233, 1628, 230), at 22k-10: (372, 367, 4032, 362)
(C) k=35: least non-excluded n (delta>=0) = 485 [14k-5=485], (delta>=1) = 761 [22k-9=761]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (243, 240, 1677, 237), at 22k-10: (383, 378, 4153, 373)
(C) k=36: least non-excluded n (delta>=0) = 499 [14k-5=499], (delta>=1) = 783 [22k-9=783]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (250, 247, 1726, 244), at 22k-10: (394, 389, 4274, 384)
(C) k=37: least non-excluded n (delta>=0) = 513 [14k-5=513], (delta>=1) = 805 [22k-9=805]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (257, 254, 1775, 251), at 22k-10: (405, 400, 4395, 395)
(C) k=38: least non-excluded n (delta>=0) = 527 [14k-5=527], (delta>=1) = 827 [22k-9=827]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (264, 261, 1824, 258), at 22k-10: (416, 411, 4516, 406)
(C) k=39: least non-excluded n (delta>=0) = 541 [14k-5=541], (delta>=1) = 849 [22k-9=849]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (271, 268, 1873, 265), at 22k-10: (427, 422, 4637, 417)
(C) k=40: least non-excluded n (delta>=0) = 555 [14k-5=555], (delta>=1) = 871 [22k-9=871]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (278, 275, 1922, 272), at 22k-10: (438, 433, 4758, 428)
(C) k=41: least non-excluded n (delta>=0) = 569 [14k-5=569], (delta>=1) = 893 [22k-9=893]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (285, 282, 1971, 279), at 22k-10: (449, 444, 4879, 439)
(C) k=42: least non-excluded n (delta>=0) = 583 [14k-5=583], (delta>=1) = 915 [22k-9=915]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (292, 289, 2020, 286), at 22k-10: (460, 455, 5000, 450)
(C) k=43: least non-excluded n (delta>=0) = 597 [14k-5=597], (delta>=1) = 937 [22k-9=937]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (299, 296, 2069, 293), at 22k-10: (471, 466, 5121, 461)
(C) k=44: least non-excluded n (delta>=0) = 611 [14k-5=611], (delta>=1) = 959 [22k-9=959]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (306, 303, 2118, 300), at 22k-10: (482, 477, 5242, 472)
(C) k=45: least non-excluded n (delta>=0) = 625 [14k-5=625], (delta>=1) = 981 [22k-9=981]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (313, 310, 2167, 307), at 22k-10: (493, 488, 5363, 483)
(C) k=46: least non-excluded n (delta>=0) = 639 [14k-5=639], (delta>=1) = 1003 [22k-9=1003]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (320, 317, 2216, 314), at 22k-10: (504, 499, 5484, 494)
(C) k=47: least non-excluded n (delta>=0) = 653 [14k-5=653], (delta>=1) = 1025 [22k-9=1025]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (327, 324, 2265, 321), at 22k-10: (515, 510, 5605, 505)
(C) k=48: least non-excluded n (delta>=0) = 667 [14k-5=667], (delta>=1) = 1047 [22k-9=1047]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (334, 331, 2314, 328), at 22k-10: (526, 521, 5726, 516)
(C) k=49: least non-excluded n (delta>=0) = 681 [14k-5=681], (delta>=1) = 1069 [22k-9=1069]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (341, 338, 2363, 335), at 22k-10: (537, 532, 5847, 527)
(C) k=50: least non-excluded n (delta>=0) = 695 [14k-5=695], (delta>=1) = 1091 [22k-9=1091]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (348, 345, 2412, 342), at 22k-10: (548, 543, 5968, 538)
(C) k=51: least non-excluded n (delta>=0) = 709 [14k-5=709], (delta>=1) = 1113 [22k-9=1113]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (355, 352, 2461, 349), at 22k-10: (559, 554, 6089, 549)
(C) k=52: least non-excluded n (delta>=0) = 723 [14k-5=723], (delta>=1) = 1135 [22k-9=1135]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (362, 359, 2510, 356), at 22k-10: (570, 565, 6210, 560)
(C) k=53: least non-excluded n (delta>=0) = 737 [14k-5=737], (delta>=1) = 1157 [22k-9=1157]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (369, 366, 2559, 363), at 22k-10: (581, 576, 6331, 571)
(C) k=54: least non-excluded n (delta>=0) = 751 [14k-5=751], (delta>=1) = 1179 [22k-9=1179]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (376, 373, 2608, 370), at 22k-10: (592, 587, 6452, 582)
(C) k=55: least non-excluded n (delta>=0) = 765 [14k-5=765], (delta>=1) = 1201 [22k-9=1201]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (383, 380, 2657, 377), at 22k-10: (603, 598, 6573, 593)
(C) k=56: least non-excluded n (delta>=0) = 779 [14k-5=779], (delta>=1) = 1223 [22k-9=1223]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (390, 387, 2706, 384), at 22k-10: (614, 609, 6694, 604)
(C) k=57: least non-excluded n (delta>=0) = 793 [14k-5=793], (delta>=1) = 1245 [22k-9=1245]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (397, 394, 2755, 391), at 22k-10: (625, 620, 6815, 615)
(C) k=58: least non-excluded n (delta>=0) = 807 [14k-5=807], (delta>=1) = 1267 [22k-9=1267]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (404, 401, 2804, 398), at 22k-10: (636, 631, 6936, 626)
(C) k=59: least non-excluded n (delta>=0) = 821 [14k-5=821], (delta>=1) = 1289 [22k-9=1289]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (411, 408, 2853, 405), at 22k-10: (647, 642, 7057, 637)
(C) k=60: least non-excluded n (delta>=0) = 835 [14k-5=835], (delta>=1) = 1311 [22k-9=1311]; not-excluded-at-target: True,True; witness (s,l,RHS,slack) at 14k-6: (418, 415, 2902, 412), at 22k-10: (658, 653, 7178, 648)
(C) mismatches with 14k-5 / 22k-9 for 3<=k<=60: []
(D) k=3 n=500: best Thm-5.3 lower bound m >= 96, /n = 0.19200; mu_k = 0.19098
(D) k=3 n=1000: best Thm-5.3 lower bound m >= 191, /n = 0.19100; mu_k = 0.19098
(D) k=3 n=2000: best Thm-5.3 lower bound m >= 382, /n = 0.19100; mu_k = 0.19098
(D) k=4 n=500: best Thm-5.3 lower bound m >= 69, /n = 0.13800; mu_k = 0.13811
(D) k=4 n=1000: best Thm-5.3 lower bound m >= 139, /n = 0.13900; mu_k = 0.13811
(D) k=4 n=2000: best Thm-5.3 lower bound m >= 277, /n = 0.13850; mu_k = 0.13811
elapsed 247.3s
