Enumeration of Balanced Ternary Designs

This page contains electronic listings of the balanced ternary designs whose classification was reported in the paper.

File structure

A complete list of the classified BTDs can be found in the file whenever the number of nonisomorphic designs is less than 1000; otherwise the first 1000 nonisomorphic designs encountered are listed. The design list is followed by

• A search summary that lists the number of (partial) designs and (partial) designs in canonical form generated per search tree level.
• A more detailed census of the design class that lists the number of nonisomorphic designs in each collection of designs with a specific b2 value and automorphism group size. The census is followed by an example design from each such collection.
• A LaTeX summary line.

The BTD classes with R<=15

The design class numbers are from the following two articles.

[1]	E. J. Billington and P.J. Robinson, A list of balanced ternary designs with R<=15, and some necessary existence conditions, Ars Combin. 16 (1983) 235-258.
[2]	T. Kunkle and D. G. Sarvate, Balanced (part) ternary designs, in: C. J. Colbourn, J. H. Dinitz (Eds.), The CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, 1996, pp. 233-238.

The links on the leftmost column of the table point to an electronic listing of the corresponding designs.

[1]	[2]	V	B	r1	r2	R	K	\Lambda	Nd	Ns	|Aut(D)|	b2
1	-	3	3	1	1	3	3	2	1	1	3	3
2	-	3	4	2	1	4	3	3	1	1	3	3
3	-	6	6	2	1	4	4	2	1	1	24	6
4	-	3	5	3	1	5	3	4	1	0	3	3
5	-	10	10	3	1	5	5	2	0	0	-	-
6	-	7	7	3	1	5	5	3	1	1	21	7
7	1	5	5	1	2	5	5	4	1	1	10	5
8	-	6	12	4	1	6	3	2	2	1	3-6	6
9	-	3	6	4	1	6	3	5	1	0	3	3
10	-	15	15	4	1	6	6	2
11	2	8	8	4	1	6	6	4	3	3	24-1152	8
12	-	5	10	2	2	6	3	2	1	1	5	10
13	-	3	6	2	2	6	3	4	2	1	3-6	6
14	3	5	6	2	2	6	5	5	1	1	10	5
15	-	3	7	5	1	7	3	6	1	0	3	3
16	-	12	14	5	1	7	6	3
17	-	21	21	5	1	7	7	2
18	4	11	11	5	1	7	7	4
19	-	9	9	5	1	7	7	5	0	0	-	-
20	-	6	14	3	2	7	3	2	2	0	2-3	12
21	-	3	7	3	2	7	3	5	2	1	3-6	6
22	5	5	7	3	2	7	5	6	1	0	10	5
23	6	4	7	1	3	7	4	5	1	1	24	6
24	7	10	10	1	3	7	7	4	1	1	120	10
25	8	7	7	1	3	7	7	6	1	1	21	7
26	-	3	8	6	1	8	3	7	1	0	3	3
27	-	12	24	6	1	8	4	2
28	-	28	28	6	1	8	8	2
29	-	19	19	6	1	8	8	3
30	9	10	10	6	1	8	8	6	2	2	160-576	10
31	-	3	8	4	2	8	3	6	2	0	3-6	6
32	-	11	22	4	2	8	4	2
33	10	6	12	4	2	8	4	4	14	6	1-48	8,10-12
34	11	5	10	4	2	8	4	5	6	6	1-20	9,10
35	12	5	8	4	2	8	5	7	1	0	10	5
36	-	14	14	4	2	8	8	4
37	13	4	8	2	3	8	4	6	2	0	2-24	6,8
38	14	7	8	2	3	8	7	7	1	1	21	7
39	-	11	11	2	3	8	8	5
40	-	9	27	7	1	9	3	2	1475	492	1-54	9
41	-	5	15	7	1	9	3	4	6	0	1-6	5
42	-	3	9	7	1	9	3	8	1	0	3	3
43	15	14	18	7	1	9	7	4
44	-	36	36	7	1	9	9	2
45	16	15	15	7	1	9	9	5
46	17	11	11	7	1	9	9	7
47	-	8	24	5	2	9	3	2	83	11	1-64	16
48	-	3	9	5	2	9	3	7	2	0	3-6	6
49	18	5	9	5	2	9	5	8	2	1	4-10	5,9
50	19	18	18	5	2	9	9	4
51	-	7	21	3	3	9	3	2	3	3	3-21	21
52	-	5	15	3	3	9	3	3	0	0	-	-
53	-	4	12	3	3	9	3	4	3	1	3-24	12
54	-	3	9	3	3	9	3	6	2	0	3	9
55	20	4	9	3	3	9	4	7	4	2	2-24	6,8,9
56	21	7	9	3	3	9	7	8	1	0	21	7
57	22	12	12	3	3	9	9	6
58	-	17	17	1	4	9	9	4
59	23	9	9	1	4	9	9	8	1	1	72	9
60	-	3	10	8	1	10	3	9	1	0	3	3
61	24	8	20	8	1	10	4	4	22539	9736	1-384	4,6-8
62	-	20	40	8	1	10	5	2
63	25	9	15	8	1	10	6	6	123	77	1-12	9
64	-	27	30	8	1	10	9	3
65	-	45	45	8	1	10	10	2
66	26	23	23	8	1	10	10	4
67	27	12	12	8	1	10	10	8
68	-	9	30	6	2	10	3	2	2465	180	1-24	18
69	-	3	10	6	2	10	3	8	2	0	3-6	6
70	-	14	35	6	2	10	4	2
71	-	19	38	6	2	10	5	2
72	-	13	26	6	2	10	5	3
73	28	10	20	6	2	10	5	4	8261	7089	1-160	12,14-20
74	29	7	14	6	2	10	5	6	718	583	1-42	8-14
75	30	5	10	6	2	10	5	9	3	2	4-10	5,9,10
76	31	12	15	6	2	10	8	6
77	-	3	10	4	3	10	3	7	2	0	3	9
78	32	4	10	4	3	10	4	8	6	2	1-24	6,8-10
79	33	12	20	4	3	10	6	4
80	34	7	10	4	3	10	7	9	6	5	1-21	7,10
81	-	22	22	4	3	10	10	4
82	-	15	15	4	3	10	10	6
83	35	13	13	4	3	10	10	7
84	36	9	18	2	4	10	5	4	14	14	1-18	18
85	37	5	10	2	4	10	5	8	6	4	4-20	10
86	-	14	20	2	4	10	7	4
87	38	9	10	2	4	10	9	9	1	1	72	9
88	-	6	22	9	1	11	3	4	141	0	1-48	6
89	-	3	11	9	1	11	3	10	1	0	3	3
90	-	15	33	9	1	11	5	3
91	39	16	22	9	1	11	8	5
92	-	55	55	9	1	11	11	2
93	-	37	37	9	1	11	11	3
94	40	28	28	9	1	11	11	4
95	41	19	19	9	1	11	11	6
96	42	13	13	9	1	11	11	9
97	-	3	11	7	2	11	3	9	2	0	3-6	6
98	43	5	11	7	2	11	5	10	3	1	4-10	5,9,10
99	44	20	22	7	2	11	10	5
100	-	9	33	5	3	11	3	2
101	-	3	11	5	3	11	3	8	2	0	3	9
102	45	4	11	5	3	11	4	9	7	0	1-24	6,8-11
103	46	7	11	5	3	11	7	10	6	5	1-21	7,10
104	47	27	27	5	3	11	11	4
105	48	14	14	5	3	11	11	8
106	49	10	22	3	4	11	5	4	9	2	1-6	22
107	50	5	11	3	4	11	5	9	6	4	4-20	10
108	51	9	11	3	4	11	9	10	3	2	8-72	9,11
109	-	18	18	3	4	11	11	6
110	52	6	11	1	5	11	6	9	1	1	60	10
111	-	26	26	1	5	11	11	4
112	-	21	21	1	5	11	11	5
113	53	11	11	1	5	11	11	10
114	-	12	48	10	1	12	3	2
115	-	3	12	10	1	12	3	11	1	0	3	3
116	-	18	54	10	1	12	4	2
117	-	30	60	10	1	12	6	2
118	-	42	63	10	1	12	8	2
119	-	48	64	10	1	12	9	2
120	-	66	66	10	1	12	12	2
121	54	27	27	10	1	12	12	5
122	55	14	14	10	1	12	12	10
123	-	11	44	8	2	12	3	2
124	-	6	24	8	2	12	3	4	1191	13	1-24	12
125	-	5	20	8	2	12	3	5	67	1	1-5	10
126	-	3	12	8	2	12	3	10	2	0	3-6	6
127	-	17	51	8	2	12	4	2
128	56	9	27	8	2	12	4	4
129	57	5	15	8	2	12	4	8	53	3	1-20	7-10
130	58	5	12	8	2	12	5	11	3	0	4-10	5,9,10
131	-	29	58	8	2	12	6	2
132	59	15	30	8	2	12	6	4
133	60	9	18	8	2	12	6	7
134	61	8	16	8	2	12	6	8	132184	116608	1-1152	8-16
135	62	24	32	8	2	12	9	4
136	63	33	33	8	2	12	12	4
137	64	17	17	8	2	12	12	8
138	-	10	40	6	3	12	3	2
139	-	7	28	6	3	12	3	3	26	26	1-21	21
140	-	4	16	6	3	12	3	6	8	1	1-24	12
141	-	3	12	6	3	12	3	9	2	0	3	9
142	-	16	48	6	3	12	4	2
143	-	11	33	6	3	12	4	3
144	65	7	21	6	3	12	4	5	109924	66403	1-168	12,14-21
145	66	6	18	6	3	12	4	6	6414	2876	1-24	12-18
146	67	4	12	6	3	12	4	10	10	1	1-24	6,8-12
147	68	10	20	6	3	12	6	6
148	69	7	14	6	3	12	6	9	6176	4963	1-168	7,9-14
149	70	7	12	6	3	12	7	11	7	0	1-21	7,10,12
150	71	14	21	6	3	12	8	6
151	-	22	22	6	3	12	12	6
152	72	19	19	6	3	12	12	7
153	73	15	15	6	3	12	12	9
154	-	9	36	4	4	12	3	2
155	-	5	20	4	4	12	3	4	7	1	2-120	20
156	-	3	12	4	4	12	3	8	3	0	3-6	12
157	74	8	24	4	4	12	4	4	449	96	1-1152	16,18-24
158	75	5	15	4	4	12	4	7	29	19	1-120	10,12-15
159	76	5	12	4	4	12	5	10	22	9	1-20	10,12
160	77	14	28	4	4	12	6	4
161	78	20	30	4	4	12	8	4
162	79	12	16	4	4	12	9	8
163	80	9	12	4	4	12	9	11	13	12	1-72	9,11,12
164	81	32	32	4	4	12	12	4
165	-	11	22	2	5	12	6	5
166	82	6	12	2	5	12	6	10	7	1	1-60	10,12
167	-	15	18	2	5	12	10	7
168	83	11	12	2	5	12	11	11
169	-	9	39	11	1	13	3	3
170	-	3	13	11	1	13	3	12	1	0	3	3
171	84	18	26	11	1	13	9	6
172	85	33	39	11	1	13	11	4
173	-	48	52	11	1	13	12	3
174	-	78	78	11	1	13	13	2
175	86	23	23	11	1	13	13	7
176	87	15	15	11	1	13	13	11
177	-	12	52	9	2	13	3	2
178	-	3	13	9	2	13	3	11	2	0	3-6	6
179	88	8	26	9	2	13	4	5
180	-	25	65	9	2	13	5	2
181	89	5	13	9	2	13	5	12	3	0	4-10	5,9,10
182	90	22	26	9	2	13	11	6
183	91	39	39	9	2	13	13	4
184	92	20	20	9	2	13	13	8
185	-	6	26	7	3	13	3	4	1101	13	1-72	18
186	-	3	13	7	3	13	3	10	2	0	3	9
187	-	12	39	7	3	13	4	3
188	93	4	13	7	3	13	4	11	10	1	1-24	6,8-12
189	94	7	13	7	3	13	7	12	101	92	1-21	7,10,12,13
190	95	31	31	7	3	13	13	5
191	-	26	26	7	3	13	13	6
192	96	16	16	7	3	13	13	10
193	-	3	13	5	4	13	3	9	3	0	3-6	12
194	97	5	13	5	4	13	5	11	88	31	1-20	10,12,13
195	98	9	13	5	4	13	9	12	298	293	1-72	9,11-13
196	-	38	38	5	4	13	13	4
197	99	12	26	3	5	13	6	5
198	100	6	13	3	5	13	6	11	23	17	1-60	10,12,13
199	101	11	13	3	5	13	11	12
200	102	4	13	1	6	13	4	9	1	0	24	12
201	-	37	37	1	6	13	13	4
202	-	25	25	1	6	13	13	6
203	103	19	19	1	6	13	13	8
204	-	17	17	1	6	13	13	9
205	104	13	13	1	6	13	13	12
206	-	3	14	12	1	14	3	13	1	0	3	3
207	105	6	21	12	1	14	4	8	230	1	1-48	5,6
208	106	10	28	12	1	14	5	6
209	107	18	42	12	1	14	6	4
210	-	42	84	12	1	14	7	2
211	-	91	91	12	1	14	14	2
212	-	61	61	12	1	14	14	3
213	-	46	46	12	1	14	14	4
214	108	37	37	12	1	14	14	5
215	109	31	31	12	1	14	14	6
216	110	21	21	12	1	14	14	9
217	-	19	19	12	1	14	14	10
218	111	16	16	12	1	14	14	12
219	-	9	42	10	2	14	3	3
220	-	3	14	10	2	14	3	12	2	0	3-6	6
221	-	20	70	10	2	14	4	2
222	112	5	14	10	2	14	5	13	3	0	4-10	5,9,10
223	113	12	28	10	2	14	6	6
224	-	41	82	10	2	14	7	2
225	114	21	42	10	2	14	7	4
226	115	17	34	10	2	14	7	5
227	116	11	22	10	2	14	7	8
228	117	9	18	10	2	14	7	10
229	-	12	56	8	3	14	3	2
230	-	3	14	8	3	14	3	11	2	0	3	9
231	118	10	35	8	3	14	4	4
232	119	4	14	8	3	14	4	12	10	0	1-24	6,8-12
233	120	9	21	8	3	14	6	8
234	121	14	28	8	3	14	7	6
235	122	7	14	8	3	14	7	13	373	344	1-21	7,10,12-14
236	123	24	42	8	3	14	8	4
237	124	25	35	8	3	14	10	5
238	125	45	45	8	3	14	14	4
239	126	23	23	8	3	14	14	8
240	127	17	17	8	3	14	14	11
241	-	6	28	6	4	14	3	4	315	0	1-18	24
242	-	3	14	6	4	14	3	10	3	0	3-6	12
243	128	5	14	6	4	14	5	12	281	70	1-24	10,12-14
244	129	20	40	6	4	14	7	4
245	130	16	28	6	4	14	8	6
246	131	27	42	6	4	14	9	4
247	132	9	14	6	4	14	9	13	10643	10508	1-72	9,11-14
248	133	30	30	6	4	14	14	6
249	134	6	14	4	5	14	6	12	257	119	1-60	10,12-14
250	135	12	21	4	5	14	8	8
251	136	18	28	4	5	14	9	6
252	137	30	42	4	5	14	10	4
253	138	11	14	4	5	14	11	13
254	-	44	44	4	5	14	14	4
255	139	6	21	2	6	14	4	6	1	1	24	21
256	140	4	14	2	6	14	4	10	2	0	2-24	12,14
257	141	19	38	2	6	14	7	4
258	142	13	26	2	6	14	7	6
259	143	10	20	2	6	14	7	8	600	493	1-120	20
260	-	9	18	2	6	14	7	9	0	0	-	-
261	144	7	14	2	6	14	7	12	39	28	1-42	14
262	145	20	28	2	6	14	10	6
263	-	33	42	2	6	14	11	4
264	146	13	14	2	6	14	13	13
265	-	35	35	2	6	14	14	5
266	147	18	18	2	6	14	14	10
267	-	15	75	13	1	15	3	2
268	-	8	40	13	1	15	3	4
269	-	5	25	13	1	15	3	7	11	0	1-6	5
270	-	3	15	13	1	15	3	14	1	0	3	3
271	-	30	90	13	1	15	5	2
272	-	60	100	13	1	15	9	2
273	148	20	30	13	1	15	10	7
274	-	105	105	13	1	15	15	2
275	149	53	53	13	1	15	15	4
276	150	27	27	13	1	15	15	8
277	151	17	17	13	1	15	15	13
278	-	14	70	11	2	15	3	2
279	-	3	15	11	2	15	3	13	2	0	3-6	6
280	-	29	87	11	2	15	5	2
281	152	15	45	11	2	15	5	4
282	153	9	27	11	2	15	5	7
283	154	8	24	11	2	15	5	8
284	155	5	15	11	2	15	5	14	3	0	4-10	5,9,10
285	156	30	50	11	2	15	9	4
286	157	24	30	11	2	15	12	7
287	-	13	65	9	3	15	3	2
288	-	9	45	9	3	15	3	3
289	-	7	35	9	3	15	3	4
290	-	5	25	9	3	15	3	6	450	0	1-6	15
291	-	4	20	9	3	15	3	8	19	0	1-24	12
292	-	3	15	9	3	15	3	12	2	0	3	9
293	158	4	15	9	3	15	4	13	10	0	1-24	6,8-12
294	-	28	84	9	3	15	5	2
295	-	19	57	9	3	15	5	3
296	159	10	30	9	3	15	5	6
297	160	7	21	9	3	15	5	9
298	161	7	15	9	3	15	7	14	981	581	1-21	7,10,12-15
299	162	28	30	9	3	15	14	7
300	-	52	52	9	3	15	15	4
301	163	35	35	9	3	15	15	6
302	164	18	18	9	3	15	15	12
303	-	12	60	7	4	15	3	2
304	-	3	15	7	4	15	3	11	3	0	3-6	12
305	165	14	42	7	4	15	5	4
306	166	5	15	7	4	15	5	13	531	77	1-24	10,12-15
307	167	15	25	7	4	15	9	8
308	168	9	15	7	4	15	9	14
309	-	11	55	5	5	15	3	2
310	-	6	30	5	5	15	3	4	24	1	1-720	30
311	-	5	25	5	5	15	3	5	0	0	-	-
312	-	3	15	5	5	15	3	10	3	0	3	15
313	169	8	30	5	5	15	4	5	35689	29363	1-128	24-28
314	-	11	33	5	5	15	5	5
315	170	6	18	5	5	15	5	10	25337	9908	1-3	16-18
316	171	14	35	5	5	15	6	5
317	172	6	15	5	5	15	6	13	5940	3977	1-60	10,12-15
318	173	21	45	5	5	15	7	4
319	174	12	20	5	5	15	9	10
320	175	26	39	5	5	15	10	5
321	176	11	15	5	5	15	11	14
322	177	32	40	5	5	15	12	5
323	-	51	51	5	5	15	15	4
324	-	41	41	5	5	15	15	5
325	-	26	26	5	5	15	15	8
326	178	21	21	5	5	15	15	10
327	179	4	15	3	6	15	4	11	4	0	2-24	12,14,15
328	180	13	39	3	6	15	5	4
329	181	9	27	3	6	15	5	6	338960	338960	1-81	27
330	182	7	21	3	6	15	5	8	5908	3269	1-168	21
331	183	5	15	3	6	15	5	12	25	6	1-10	15
332	184	10	25	3	6	15	6	7	0	0	-	-
333	-	8	20	3	6	15	6	9	0	0	-	-
334	185	14	30	3	6	15	7	6
335	186	7	15	3	6	15	7	13	39	28	1-42	14
336	187	13	15	3	6	15	13	14
337	-	34	34	3	6	15	15	6
338	-	23	23	3	6	15	15	9
339	-	19	19	3	6	15	15	11
340	188	8	15	1	7	15	8	13	4	4	12-1344	14
341	-	12	18	1	7	15	10	11
342	189	50	50	1	7	15	15	4
343	-	29	29	1	7	15	15	7
344	190	15	15	1	7	15	15	14