Cyclic Difference Sets with k<=100

vklambdanStatusComment
7 3 1 2EXISTS
13 4 1 3EXISTS
11 5 2 3EXISTS
21 5 1 4EXISTS
16 6 2 4NOLander Theorem 4.31
31 6 1 5EXISTS
15 7 3 4EXISTS
57 8 1 7EXISTSSinger difference set
19 9 4 5EXISTSType Q
25 9 3 6NOMann test
37 9 2 7EXISTS
73 9 1 8EXISTSSinger difference set
31 10 3 7NOLander Theorem 4.38
91 10 1 9EXISTS
23 11 5 6EXISTSType Q
56 11 2 9NOLander Theorem 4.19
45 12 3 9NOTuryn test
133 12 1 11EXISTS
27 13 6 7NOLander Theorem 4.38
40 13 4 9EXISTS
79 13 2 11NOLander Theorem 4.38
183 14 1 13EXISTS
31 15 7 8EXISTSTypes H6, Q
36 15 6 9NOTuryn test
71 15 3 12NOLander Theorem 4.38
41 16 6 10NOMann test
49 16 5 11NOLander Theorem 4.38
61 16 4 12NOMann test
81 16 3 13NOLander Theorem 4.38
121 16 2 14NOMann test
35 17 8 9EXISTS
69 17 4 13NOLander Theorem 4.38
273 17 1 16EXISTSSinger difference set
154 18 2 16NOLander Theorem 4.27
307 18 1 17EXISTSSinger difference set
39 19 9 10NOMann test
115 19 3 16NOcontracted multiplier test
96 20 4 16NOTuryn test
191 20 2 18NOLander Theorem 4.38
381 20 1 19EXISTS
43 21 10 11EXISTSTypes H_6, Q
71 21 6 15NONO (Lander, but proof is wrong)
85 21 5 16EXISTSSinger difference set
78 22 6 16NOLander Theorem 4.19
155 22 3 19NOMann test
47 23 11 12EXISTSType Q
70 24 8 16NOLander Theorem 4.27
139 24 4 20NOMann test
553 24 1 23EXISTS
51 25 12 13NOMann test
61 25 10 15NOMann test
101 25 6 19EXISTS
121 25 5 20NOMann test
201 25 3 22NOMann test
301 25 2 23NONO (Lander, but proof is wrong)
66 26 10 16NOTuryn test
131 26 5 21NOLander Theorem 4.38
651 26 1 25EXISTSSinger difference set
55 27 13 14NOMann test
79 27 9 18NOMann test
352 27 2 25NOSchmidt test
64 28 12 16NOLander Theorem 4.31
85 28 9 19NOMann test
109 28 7 21EXISTS
127 28 6 22NOcontracted multiplier test
253 28 3 25NONO (Lander, exercise)
757 28 1 27EXISTSSinger difference set
59 29 14 15EXISTSType Q
204 29 4 25NOLander Theorem 4.19
407 29 2 27NOMann test
175 30 5 25NOTuryn test
291 30 3 27NOMann test
871 30 1 29EXISTS
63 31 15 16EXISTSTwo sets exist
156 31 6 25EXISTSSinger difference set
249 32 4 28NOMann test
993 32 1 31EXISTSSinger difference set
67 33 16 17EXISTSType Q
97 33 11 22NOMann test
133 33 8 25EXISTS
177 33 6 27NOLander Theorem 4.38
265 33 4 29NOMann test
529 33 2 31NOLander Theorem 4.38
1057 33 1 32EXISTSSinger difference set
103 34 11 23NONO (Lander, exercise)
375 34 3 31NOSchmidt test
71 35 17 18EXISTSType Q
120 35 10 25NOLander Theorem 4.33
171 35 7 28NOMann test
239 35 5 30NOLander Theorem 4.38
85 36 15 21NOMann test
127 36 10 26NOcontracted multiplier test
141 36 9 27NOLander Theorem 4.38
253 36 5 31NOLander Theorem 4.38
75 37 18 19NOMann test
112 37 12 25NOLander Theorem 4.19
149 37 9 28NOMann test
223 37 6 31NOLander Theorem 4.38
704 38 2 36NOTuryn test
1407 38 1 37EXISTS
79 39 19 20EXISTS
495 39 3 36NOLander Theorem 4.19
105 40 15 25NOTuryn test
121 40 13 27EXISTS
131 40 12 28NOMann test
391 40 4 36NOcontracted multiplier test
521 40 3 37NOMann test
83 41 20 21EXISTS
165 41 10 31NONO (Lander, exercise)
329 41 5 36NOcontracted multiplier test
411 41 4 37NOMann test
288 42 6 36NOTuryn test
575 42 3 39NOMann test
1723 42 1 41EXISTSSinger difference set
87 43 21 22NOMann test
259 43 7 36NOMann test
1893 44 1 43EXISTSSinger difference set
91 45 22 23NOMann test
100 45 20 25NOLander Theorem 4.33
111 45 18 27NOMann test
221 45 9 36NOLander Theorem 4.19
991 45 2 43NOLander Theorem 4.38
139 46 15 31NOLander Theorem 4.38
208 46 10 36NOTuryn test
231 46 9 37NONO (Lander, exercise)
415 46 5 41NOArasu p-adic square test
691 46 3 43NOLander Theorem 4.38
95 47 23 24NOMann test
189 48 12 36NOTuryn test
565 48 4 44NOMann test
1129 48 2 46NOMann test
2257 48 1 47EXISTSSinger difference set
99 49 24 25NOSchmidt test
113 49 21 28NOMann test
169 49 14 35NOMann test
197 49 12 37EXISTS
295 49 8 41NOLander Theorem 4.38
337 49 7 42NOMann test
393 49 6 43NOLander Theorem 4.38
589 49 4 45NOMann test
785 49 3 46NOMann test
1177 49 2 47NOArasu p-adic square test
176 50 14 36NOTuryn test
351 50 7 43NOMann test
491 50 5 45NONO (Lander, exercise)
2451 50 1 49EXISTSSinger difference set
103 51 25 26EXISTS
171 51 15 36NOMann test
511 51 5 46NOMann test
851 51 3 48NOMann test
1276 51 2 49NOcontracted multiplier test
205 52 13 39NOMann test
885 52 3 49NOcontracted multiplier test
1327 52 2 50NOMann test
107 53 26 27EXISTS
690 53 4 49NOLander Theorem 4.19
1379 53 2 51NOMann test
160 54 18 36NOTuryn test
319 54 9 45NOMann test
2863 54 1 53EXISTSSinger difference set
111 55 27 28NOcontracted multiplier test
271 55 11 44NOLander Theorem 4.38
496 55 6 49NOcontracted multiplier test
991 55 3 52NOLander Theorem 4.38
155 56 20 36NOLander Theorem 4.19
281 56 11 45NOMann test
441 56 7 49NOSchmidt test
771 56 4 52NOMann test
115 57 28 29NOMann test
153 57 21 36NOTuryn test
169 57 19 38NOMann test
400 57 8 49EXISTSSinger difference set
457 57 7 50NOMann test
799 57 4 53NOMann test
1065 57 3 54NOMann test
119 59 29 30NOMann test
591 60 6 54NOMann test
709 60 5 55NOMann test
3541 60 1 59EXISTSSinger difference set
123 61 30 31NOMann test
306 61 12 49NOLander Theorem 4.19
611 61 6 55NOMann test
1831 61 2 59NOLander Theorem 4.38
3783 62 1 61EXISTSSinger difference set
127 63 31 32EXISTSTypes Q, H6, Singer
280 63 14 49NOLander Theorem 4.33
559 63 7 56NOMann test
145 64 28 36NOMann test
169 64 24 40NOMann test
193 64 21 43NOMann test
225 64 18 46NOMann test
253 64 16 48NOcontracted multiplier test
289 64 14 50NOMann test
449 64 9 55NOMann test
505 64 8 56NOMann test
577 64 7 57NOMann test
673 64 6 58NOMann test
1009 64 4 60NOMann test
1345 64 3 61NOArasu p-adic square test
2017 64 2 62NOMann test
131 65 32 33EXISTS
209 65 20 45NOcontracted multiplier test
261 65 16 49NOSchmidt test
321 65 13 52NOMann test
1041 65 4 61NOLander Theorem 4.38
2081 65 2 63NOMann test
4161 65 1 64EXISTSSinger difference set
144 66 30 36NOTuryn test
287 66 15 51NOMann test
331 66 13 53NOLander Theorem 4.38
391 66 11 55NOMann test
859 66 5 61NONO (Baumert)
1431 66 3 63NOMann test
2146 66 2 64NOTuryn test
135 67 33 34NOMann test
1475 67 3 64NOLander Theorem 4.19
1140 68 4 64NOLander Theorem 4.19
2279 68 2 66NOMann test
4557 68 1 67EXISTSSinger difference set
139 69 34 35EXISTSType Q
277 69 17 52NOMann test
783 69 6 63NOTuryn test
2347 69 2 67NOLander Theorem 4.38
211 70 23 47NOLander Theorem 4.38
231 70 21 49NOLander Theorem 4.33
691 70 7 63NOMann test
806 70 6 64NOLander Theorem 4.19
1611 70 3 67NOLander Theorem 4.38
143 71 35 36EXISTS
711 71 7 64NOcontracted multiplier test
569 72 9 63NOMann test
640 72 8 64NOTuryn test
1279 72 4 68NOLander Theorem 4.38
1705 72 3 69NOMann test
5113 72 1 71EXISTSSinger difference set
147 73 36 37NOLander Theorem 4.38
220 73 24 49NOLander Theorem 4.19
585 73 9 64EXISTSSinger difference set
2629 73 2 71NOArasu p-adic square test
5403 74 1 73EXISTSSinger difference set
151 75 37 38EXISTSType Q
223 75 25 50NOMann test
371 75 15 60NOMann test
1111 75 5 70NOMann test
191 76 30 46NOLander Theorem 4.38
301 76 19 57NOMann test
381 76 15 61NOArasu p-adic square test
476 76 12 64NOLander Theorem 4.27
951 76 6 70NOMann test
1141 76 5 71NOArasu p-adic square test
155 77 38 39NOMann test
210 77 28 49NOLander Theorem 4.33
2927 77 2 75NOMann test
287 78 21 57NOMann test
430 78 14 64NOLander Theorem 4.19
547 78 11 67NOLander Theorem 4.38
2003 78 3 75NOMann test
159 79 39 40NOMann test
2055 79 3 76NOMann test
396 80 16 64NOTuryn test
791 80 8 72NOMann test
1581 80 4 76NOMann test
6321 80 1 79EXISTSSinger difference set
163 81 40 41EXISTSType Q
181 81 36 45NOcontracted multiplier test
217 81 30 51NOMann test
241 81 27 54NOMann test
325 81 20 61NOSchmidt test
361 81 18 63NOMann test
433 81 15 66NOMann test
649 81 10 71NOArasu p-adic square test
721 81 9 72NOMann test
811 81 8 73NOLander Theorem 4.38
1081 81 6 75NOMann test
1297 81 5 76NOMann test
2161 81 3 78NOMann test
3241 81 2 79NOLander Theorem 4.38
370 82 18 64NOTuryn test
739 82 9 73NOLander Theorem 4.38
2215 82 3 79NOMann test
6643 82 1 81EXISTSSinger difference set
167 83 41 42EXISTS
3404 83 2 81NOLander Theorem 4.19
333 84 21 63NOTuryn test
2325 84 3 81NOLander Theorem 4.27
3487 84 2 82NOMann test
6973 84 1 83EXISTSSinger difference set
171 85 42 43NOArasu p-adic square test
239 85 30 55NOLander Theorem 4.38
341 85 21 64EXISTSSinger difference set
421 85 17 68NOMann test
511 85 14 71NOMann test
1191 85 6 79NOArasu p-adic square test
1429 85 5 80NOMann test
1786 85 4 81NOcontracted multiplier test
3571 85 2 83NOLander Theorem 4.38
1463 86 5 81NOLander Theorem 4.19
175 87 43 44NOSchmidt test
1248 87 6 81NOLander Theorem 4.27
2495 87 3 84NOMann test
265 88 29 59NOMann test
320 88 24 64NOTuryn test
639 88 12 76NOLander Theorem 4.38
697 88 11 77NOMann test
179 89 44 45EXISTS
357 89 22 67NOMann test
980 89 8 81NOLander Theorem 4.19
1959 89 4 85NOMann test
891 90 9 81NOSchmidt test
8011 90 1 89EXISTSSinger difference set
183 91 45 46NOMann test
196 91 42 49NOTuryn test
211 91 39 52NOMann test
391 91 21 70NOMann test
547 91 15 76NOMann test
820 91 10 81EXISTSSinger difference set
1639 91 5 86NOMann test
300 92 28 64NOLander Theorem 4.19
599 92 14 78NOLander Theorem 4.38
645 92 13 79NOMann test
187 93 46 47NOMann test
714 93 12 81NOLander Theorem 4.19
1427 93 6 87NOLander Theorem 4.38
283 94 31 63NOMann test
2915 94 3 91NOMann test
191 95 47 48EXISTSType Q
471 95 19 76NOLander Theorem 4.19
241 96 38 58NOMann test
286 96 32 64NOLander Theorem 4.27
457 96 20 76NOMann test
571 96 16 80NOMann test
609 96 15 81NOLander Theorem 4.27
913 96 10 86NOMann test
1521 96 6 90NOMann test
2281 96 4 92NOMann test
4561 96 2 94NOMann test
195 97 48 49NOLander Theorem 4.19
389 97 24 73NOcontracted multiplier test
583 97 16 81NOLander Theorem 4.19
1165 97 8 89NOMann test
2329 97 4 93NOMann test
3105 97 3 94NOMann test
9507 98 1 97EXISTSSinger difference set
199 99 49 50EXISTS
540 99 18 81NOLander Theorem 4.32
1079 99 9 90NOMann test
1387 99 7 92NOMann test
221 100 45 55NOMann test
276 100 36 64NOLander Theorem 4.27
301 100 33 67NOLander Theorem 4.38
397 100 25 75NOMann test
551 100 18 82NOMann test
661 100 15 85NOMann test
901 100 11 89NOMann test
991 100 10 90NOMann test
1101 100 9 91NOArasu p-adic square test
1981 100 5 95NOMann test
4951 100 2 98NOMann test