Cyclic Difference Sets with k<=100

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