The best known packings of unequal circles in a circle

N	radius	ratio	density	contacts	loose	boundary	core	reference
1	1.000000000000	1.0000000000	1.000000000000	1		1
2	0.666666666667	3.0000000000	0.555555555556	3		0	2
3	0.600000000000	5.0000000000	0.560000000000	3	1	1	2
4	0.571428571429	7.0000000000	0.612244897960	3	2	1	3
5	0.555469288333	9.0013977461	0.678801486618	6	2	5		[1]
6	0.542640687119	11.0570403997	0.744326702608	6	3	5	1	[2]
7	0.519977897050	13.4621106776	0.772505752631	10	2	7		[3]
8	0.493165141801	16.2217466766	0.775237794466	12	2	7	1	[3]
9	0.467941000492	19.2331939081	0.770445707200	12	3	8	1	[3]
10	0.454541466714	22.0001930127	0.795440588106	10	5	9	1	[4]
11	0.440693929196	24.9606342889	0.812155673144	14	4	10	1	[3]
12	0.422961308500	28.3713894364	0.807517878594	12	6	11	1	[4]
13	0.412098358012	31.5458670176	0.822998351584	16	5	12	1	[4]
14	0.398909868871	35.0956471436	0.824061325180	22	3	10	4	[5]
15	0.386219726423	38.8379955082	0.822068620343	14	8	13	2	[5]
16	0.376841964345	42.4581164357	0.829870154972	18	7	14	2	[32]
17	0.367239298376	46.2913421172	0.832987866973	16	9	14	3	[5]
18	0.359139769580	50.1197626235	0.839573203594	20	8	14	4	[6]
19	0.350293089177	54.2402935914	0.839562225382	20	9	15	4	[5]
20	0.342462425681	58.4005674790	0.841487680797	28	6	13	7	[7]
21	0.335683774638	62.5588770939	0.846021288424	26	8	14	7	[6]
22	0.329537232966	66.7602862414	0.851481859755	26	9	17	5	[5]
23	0.323036150563	71.1994616079	0.852967072144	30	8	18	5	[6]
24	0.316835269443	75.7491425819	0.853966112880	26	11	17	7	[11]
25	0.311387317984	80.2858644400	0.857144626324	34	8	18	7	[7]
26	0.305960855061	84.9781910657	0.858710488148	34	9	15	11	[27]
27	0.300832427789	89.7509626820	0.860310064187	32	11	16	11	[11]
28	0.296215183171	94.5258771015	0.863332723968	28	14	20	8	[11]
29	0.291506764758	99.4831115636	0.864413006912	38	10	18	11	[11]
30	0.286970495601	104.5403637652	0.865154197601	46	7	17	13	[28]
31	0.282771273549	109.6292406611	0.866658816021	38	12	19	12	[27]
32	0.278746094616	114.7998146630	0.868047819745	40	12	17	15	[28]
33	0.274849612282	120.0656596383	0.869118084589	42	12	18	15	[11]
34	0.271203877318	125.3669392055	0.870720473134	34	17	22	12	[11]
35	0.267483732649	130.8490787587	0.870835860590	46	12	21	14	[29]
36	0.264107928757	136.3079108204	0.872235405952	44	14	20	16	[27]
37	0.260960824666	141.7837334298	0.874263843374	40	17	23	14	[27]
38	0.257710780360	147.4521164651	0.874753436319	48	14	20	18	[11]
39	0.254569617068	153.1997433521	0.875153761502	42	18	26	13	[30]
40	0.251644994145	158.9540858379	0.876262497595	48	16	26	14	[33]
41	0.248777002525	164.8062304148	0.877026542644	60	11	25	16	[30]
42	0.246048849401	170.6978110333	0.878070764467	52	16	24	18	[30]
43	0.243305345567	176.7326562420	0.878325566835	38	24	26	17	[30]
44	0.240736277435	182.7726193526	0.879187844203	60	14	24	20	[30]
45	0.238139377034	188.9649690047	0.879220663240	56	17	26	19	[30]
46	0.235651027882	195.2039013515	0.879448477327	58	17	30	16	[30]
47	0.233266603647	201.4861933308	0.879874773754	58	18	26	21	[30]
48	0.230990400294	207.8008434073	0.880568588810	66	15	28	20	[30]
49	0.228778537727	214.1809301120	0.881228284544	50	24	27	22	[30]
50	0.226690133360	220.5654002624	0.882339112380	62	19	31	19	[11,31]
51	0.224065624360	227.6118889083	0.878758640295	58	22	27	24	[32]
52	0.222003637260	234.2303965905	0.879084766777	76	14	25	27	[35]
53	0.219996300324	240.9131422751	0.879389290312	64	21	33	20	[35]
54	0.218152316295	247.5334707287	0.880569896493	68	20	27	27	[32]
55	0.216119453948	254.4888902654	0.879801684296	70	20	28	27	[32]
56	0.214219570324	261.4140244768	0.879695376722	76	18	26	30	[35]
57	0.212402732101	268.3581300305	0.879872866750	60	27	29	28	[32]
58	0.210789945656	275.1554388395	0.881370302911	68	24	29	29	[35]
59	0.209049231200	282.2301697134	0.881438668943	80	19	29	30	[35]
60	0.207583470150	289.0403554611	0.883483087066	70	25	30	30	[32]
61	0.205933088040	296.2127192889	0.883624969001	86	18	29	32	[35]
62	0.204170116877	303.6683376993	0.882453799536	96	14	24	38	[35]
63	0.202622167431	310.9235322023	0.882807081863	72	27	31	32	[32]
64	0.201116726300	318.2231591442	0.883218637388	86	21	30	34	[35]
65	0.199651070037	325.5680021542	0.883677726374	76	27	30	35	[32]
66	0.198262542330	332.8919281694	0.884530065767	72	30	34	32	[32]
67	0.196806455117	340.4359880387	0.884494844576	92	21	32	35	[35]
68	0.195409713982	347.9867945882	0.884711745292	102	17	25	43	[35]
69	0.194034910001	355.6061123203	0.884855278965	80	29	33	36	[32]
70	0.192862925372	362.9520804209	0.886595802429	88	26	34	36	[35]
71	0.191339205566	371.0687508599	0.884844320603	102	20	35	36	[35]
72	0.190100078662	378.7478706300	0.885465630603	92	26	33	39	[35]
73	0.188797898330	386.6568465306	0.885256766417	106	20	34	39	[35]
74	0.187652229447	394.3465005357	0.886282182978	102	23	30	44	[35]
75	0.186530049324	402.0799880334	0.887310530967	98	26	36	39	[35]
76	0.185357830183	410.0177474292	0.887644746712	86	33	38	38	[32]
77	0.184183912408	418.0603994857	0.887743933551	106	24	33	44	[35]
78	0.182959781717	426.3232021158	0.887139991980	104	26	35	43	[35]
79	0.181803788385	434.5343994310	0.886981633399	112	23	32	47	[35]
80	0.180797827391	442.4831932676	0.888088143944	106	27	34	46	[35]
81	0.179643777864	450.8923212532	0.887543293508	116	23	29	52	[35]
82	0.178719435871	458.8197114672	0.889079309761	108	28	39	43	[35]
83	0.177624417057	467.2780993459	0.888733898853	112	27	36	47	[35]
84	0.176580836418	475.7028095683	0.888714432668	108	30	34	50	[35]
85	0.175519993297	484.2753147581	0.888336635091	112	29	35	50	[35]
86	0.174561063816	492.6642752977	0.888813032602	100	36	41	45	[35]
87	0.173564143975	501.2556050329	0.888730815965	124	25	37	50	[35]
88	0.172608841845	509.8232457804	0.888905160790	126	25	32	56	[35]
89	0.171722472336	518.2781192774	0.889628215185	112	33	37	52	[35]
90	0.170842299992	526.8016176568	0.890260339899	108	36	41	49	[32]
91	0.169908154501	535.5834760683	0.890173619675	110	36	39	52	[32]
92	0.169048585789	544.2222398393	0.890714829836	130	27	35	57	[35]
93	0.168145184781	553.0934479101	0.890643967805	106	40	38	55	[32]
94	0.167269807352	561.9663314498	0.890720440867	140	24	33	61	[35]
95	0.166459135225	570.7106424143	0.891343317334	124	33	39	56	[35]
96	0.165564282566	579.8352066764	0.890922368469	132	30	39	57	[35]
97	0.164812382141	588.5480128356	0.891902488280	138	28	39	58	[35]
99	0.163202604980	606.6079644498	0.892320364343	132	33	36	63	[35]
100	0.162386149659	615.8160668874	0.892203966272	114	43	43	57	[32]
101	0.161571750169	625.1092774207	0.891978618739	150	26	33	68	[35]
102	0.160772055399	634.4386140185	0.891786290728	124	40	41	61	[35]
103	0.159938775645	643.9964266607	0.891092408681	150	28	41	62	[35]
104	0.159294159135	652.8801844647	0.892381789030	128	40	42	62	[35]
105	0.158557176990	662.2216792295	0.892523337673	138	36	41	64	[35]
106	0.157702337821	672.1523692332	0.891215084009	118	47	44	62	[32]
107	0.156974221138	681.6405854696	0.891217818823	142	36	40	67	[35]
108	0.156382455301	690.6145564206	0.892662479830	138	39	43	65	[35]
109	0.155668860503	700.2042646679	0.892611636998	146	36	43	66	[35]
110	0.154979545043	709.7710860461	0.892729898928	142	39	37	73	[35]
111	0.154296471241	719.3942875519	0.892813285749	154	34	44	67	[35]
112	0.153654173367	728.9095866761	0.893265188913	124	50	49	63	[32]
113	0.153137421641	737.8993245986	0.895083756716	150	38	46	67	[35]
114	0.152236214785	748.8362749995	0.892304688894	162	33	42	72	[35]
115	0.151681159211	758.1693111953	0.893478603040	156	37	43	72	[35]
116	0.151060666845	767.9034021398	0.893789684873	146	43	41	75	[35]
117	0.150453449066	777.6491713981	0.894163738620	158	38	43	74	[35]
118	0.149778960864	787.8276048873	0.893642214583	144	46	49	69	[32]
119	0.149184148617	797.6718780299	0.893976897058	142	48	45	74	[35]
120	0.148567956499	807.7111836725	0.893964382950	156	42	47	73	[35]
121	0.147886669501	818.1940969276	0.893074194434	138	52	44	77	[32]
122	0.147388947763	827.7418480278	0.894313839396	154	45	50	72	[35]
123	0.146821173141	837.7538291538	0.894622169919	156	45	44	79	[35]
124	0.146294678036	847.6043125074	0.895351322677	168	40	45	79	[35]
125	0.145664418945	858.1368113436	0.894725808416	164	43	45	80	[35]
126	0.145106446849	868.3280635415	0.894902790676	178	37	44	82	[35]
127	0.144514628994	878.8037646021	0.894579214830	144	55	49	78	[32]
128	0.144063986076	888.4940885375	0.895926675635	152	52	50	78	[35]
129	0.143480695276	899.0756544042	0.895548479206	178	40	45	84	[35]
130	0.142886243063	909.8146694425	0.894948480653	182	39	44	86	[35]
131	0.142377706518	920.0878649058	0.895346456934	164	49	51	80	[35]
132	0.141820353032	930.7549810598	0.895054452984	182	41	46	86	[35]
133	0.141326960604	941.0801692134	0.895495084960	182	42	47	86	[35]
134	0.140864777521	951.2668983559	0.896261677369	150	59	53	81	[32]
135	0.140356131481	961.8389918270	0.896367206605	192	39	44	91	[35]
136	0.139845123479	972.5044150034	0.896370817199	176	48	51	85	[35]
137	0.139326214815	983.3038253563	0.896201444539	148	63	56	81	[32]
138	0.138891118974	993.5840464089	0.897042844231	188	44	50	88	[35]
139	0.138333822180	1004.8157262623	0.896237149610	170	54	52	87	[35]
140	0.137886863875	1015.3251445848	0.896792431915	184	48	51	89	[35]
141	0.137347902807	1026.5901198232	0.896083502659	188	47	48	93	[35]
142	0.136812397663	1037.9176333846	0.895348707098	194	45	50	92	[35]
143	0.136456780567	1047.9508559839	0.896906853197	164	61	52	91	[32]
144	0.136014323995	1058.7120221664	0.897266384006	198	45	51	93	[35]
145	0.135501167812	1070.1014783933	0.896628767133	184	53	50	95	[35]
146	0.135001784056	1081.4671896447	0.896106988844	200	46	52	94	[35]
147	0.134604177751	1092.0909176524	0.896875633341	208	43	47	100	[35]
148	0.134197078268	1102.8556054325	0.897461595051	202	47	51	97	[35]
149	0.133721480741	1114.2562823463	0.897071961248	192	53	55	94	[35]
150	0.133338593597	1124.9556182786	0.897868372034	196	52	52	98	[35]
151	0.132872130339	1136.4309401434	0.897482140317	190	56	54	97	[32]
152	0.132449133927	1147.6103730818	0.897624457985	206	49	45	107	[35]
153	0.132000255400	1159.0886664300	0.897358452887	176	65	56	97	[32]
154	0.131627906198	1169.9646712328	0.898078195915	168	70	58	96	[32]
155	0.131257885457	1180.8814339797	0.898778853886	214	48	52	103	[35]
156	0.130743269848	1193.1780517755	0.897442899663	174	69	59	97	[32]
157	0.130391161493	1204.0693418312	0.898282720946	192	61	56	101	[35]
158	0.129891996762	1216.3951893780	0.897042119475	186	65	53	105	[32]
159	0.129583620644	1227.0069257967	0.898385040135	178	70	57	102	[32]
160	0.129236802487	1238.0374391856	0.899149866548	212	54	53	107	[35]
161	0.128789539180	1250.1015301775	0.898465879832	224	49	48	113	[35]
162	0.128333050053	1262.3404488002	0.897597703407	208	58	57	105	[35]
163	0.127996820672	1273.4691310669	0.898361456319	206	60	61	102	[35]
164	0.127624131936	1285.0234317928	0.898566753822	204	62	55	109	[35]
165	0.127188295103	1297.2891873905	0.897832204090	214	58	57	108	[35]
166	0.126846718525	1308.6660966062	0.898379513080	214	59	54	112	[35]
167	0.126421105571	1320.9819614037	0.897688238677	190	72	61	106	[32]
168	0.126073666756	1332.5542464402	0.898058942308	188	74	58	110	[32]
169	0.125748187366	1343.9557542696	0.898698737527	212	63	50	119	[35]
170	0.125364168676	1356.0493544161	0.898456733385	192	74	62	108	[32]
171	0.125064209148	1367.2976558608	0.899375988257	196	73	59	112	[35]
172	0.124687714879	1379.4462443030	0.899151415923	202	71	60	112	[35]
173	0.124307778649	1391.7069541439	0.898830872994	196	75	61	112	[32]
174	0.123990417421	1403.3342545327	0.899371707002	242	53	51	123	[35]
175	0.123668568186	1415.0725812301	0.899806550514	236	57	53	122	[35]
176	0.123318516671	1427.1984836633	0.899788913770	222	65	59	117	[35]
177	0.122911327712	1440.0625499257	0.898892296789	232	61	58	119	[35]
178	0.122612039183	1451.7334609693	0.899531186978	224	66	58	120	[35]
179	0.122287918906	1463.7586574513	0.899766419765	214	72	59	120	[35]
180	0.121917829244	1476.4042397750	0.899283166721	206	77	59	121	[32]
181	0.121637160801	1488.0321014417	0.900079222942	234	64	53	128	[35]
182	0.121282230952	1500.6320264029	0.899737185610	230	67	55	127	[35]
183	0.120945925383	1513.0728829481	0.899630209633	244	61	54	129	[35]
184	0.120609137234	1525.5892233309	0.899475715939	224	72	60	124	[35]
185	0.120344702362	1537.2508832463	0.900363393477	208	81	61	124	[32]
186	0.120048886760	1549.3688031620	0.900746364508	246	63	60	126	[35]
187	0.119650831277	1562.8809094279	0.899554955866	214	80	60	127	[32]
188	0.119380739888	1574.7933894217	0.900248874591	228	74	60	128	[35]
189	0.119036301390	1587.7509448260	0.899784701856	264	57	48	141	[35]
190	0.118724525107	1600.3433143186	0.899775935496	250	65	60	130	[35]
191	0.118402847864	1613.1368750470	0.899579772720	224	79	59	132	[32]
192	0.118121994269	1625.4381852272	0.899968068501	226	79	61	131	[35]
193	0.117808264268	1638.2551869232	0.899820017392	228	79	63	130	[35]
194	0.117516113032	1650.8374468374	0.899965930536	222	83	61	133	[32]
195	0.117259213228	1662.9823331706	0.900618614092	252	69	59	136	[35]
196	0.116973039841	1675.5997815157	0.900788861536	250	71	54	142	[35]
197	0.116656429526	1688.7196085113	0.900455322015	244	75	61	136	[35]
198	0.116381763645	1701.2974696319	0.900734942727	256	70	65	133	[35]
199	0.116075026825	1714.4083912211	0.900484309735	230	84	68	131	[32]
200	0.115859964556	1726.2218296583	0.901625044431	224	88	63	137	[32]
300	0.094723794939	3167.1028403428	0.901751016209	360	120	79	221	[32]
400	0.082214020508	4865.3501863383	0.904601744648	446	177	89	311	[32]
600	0.067286779611	8917.0562697245	0.907767155081	682	259	116	484	[32]
800	0.058326432688	13715.9082621131	0.908894428470	902	349	139	661	[32]
1000	0.052193175911	19159.5928500688	0.909405055040	1135	431	161	839	[32]
2000	0.036953992134	54121.3515647600	0.911081268989	2369	789	221	1779	[32]

23-Mar-2011:	First complete presentation from N=1 to N=100.
31-Mar-2011:	André Müller [26] sent me three excellent packings for N=60, 100 and 200. The last is the densest circle packing I have ever seen!
19-Jan-2012:	What a surprise! Tao Ye [27] sent me twelve improved packings for N=26, 31, 32, 35, 36, 37, 39, 40, 43, 44, 47 and 48. After the long time since Al Zimmermann's contest has been finished it is unbelievable that such improvements are possible. Great result!
20-Jan-2012:	Some of the new record packings, namely for N=35, 36, 37, 39 and 40, could be improved by applying simple exchange heuristics. Nevertheless, the credits should be given to Tao Ye and Wenqi Huang. For comparison, see here.
08-Mar-2012:	Better packings were found for N=58, 63, 64, 67, 69, 71, 75, 78, 79, 80, 81, 82, 83, 84, 86, 88, 94 and 99 by Eckard Specht [31].
08-Mar-2012:	Zhanghua Fu and Wenqi Huang [28] sent me two nice improvements for N=30 and 100.
08-Mar-2012:	Unbelievable how some packings of this old famous contest can be improved nowadays, today for N=35, 36, 37, 39, 40, 42 and 46 by Tao Ye and Wenqi Huang [27].
09-Mar-2012:	Some minor improvements for N=52, 54, 61, 63, 70, 78, 79, 84 and 85 by Eckard Specht [31].
09-Mar-2012:	Further astonishing improvements for N=32, 36, 37, 41 and 60 by Zhanghua Fu and Wenqi Huang [28].
09-Mar-2012:	A tiny improvement for N=60. The credits should be given to Zhanghua Fu and Wenqi Huang [28].
11-Mar-2012:	Three new records for N=40, 43 and 45 by Tao Ye and Wenqi Huang [27].
13-Mar-2012:	Nearly all of the packings in the range 51 ≤ N ≤ 100, namely for N=51, 52, 53, 55, 56, 57, 58, 59, 62, 64, 65, 66, 67, 68, 70, 72, 73, 74, 75, 76, 77, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98 and 99, could be improved by Zhanghua Fu and Wenqi Huang [28]. That's great!
14-Mar-2012:	But all these packings are still far from the putative optima, so improvements were found for N= 51, 52, 53, 55, 56, 57, 60, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 74, 77, 79, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 96, 97, 98 and 99 by Eckard Specht [31].
14-Mar-2012:	Again, three new records for N=41, 46 and 48 by Tao Ye and Wenqi Huang [27]. Tao Ye was the first who sent me the coordinates in the new format right off, thanks!
22-Mar-2012:	Yet another record for N=36 by Tao Ye and Wenqi Huang [27], but ...
23-Mar-2012:	... this was not the last word: a better packing by Tao Ye and Wenqi Huang [27].
18-Apr-2012:	An essential improvement for N=35 by Tao Ye and Wenqi Huang [27].
24-Sep-2012:	Four new record packings for N=41, 42, 45 and 46 by Tao Ye and Wenqi Huang [27].
27-Sep-2012:	More new record packings for N=35, 37, 39 and 44 by Zhizhong Zeng, Wenqi Huang and Zhanghua Fu [29].
02-Oct-2012:	Motivated by a question Tao Ye and Wenqi Huang [27] came up with 48 new record packings for N=51–99 (except N=58). Great!
17-Dec-2012:	Two new record packings for N=41 and 43 went to Zhizhong Zeng, Wenqi Huang and Zhanghua Fu [29].
05-Feb-2013:	Five new record packings for N=37, 39, 43, 44 and 49 by Tao Ye and Wenqi Huang [27].
06-Mar-2013:	Four new record packings for N=45, 46, 47 and 48 by Zhizhong Zeng, Wenqi Huang and Zhanghua Fu [29].
21-Mar-2013:	A new record packing once more for N=48 by Zhizhong Zeng, Wenqi Huang and Zhanghua Fu [29].
25-Mar-2013:	Four new record packings for N=45, 46, 47 and 48 by Tao Ye and Wenqi Huang [27].
17-Jul-2014:	After 16 months, all packings for N=39–49 are completely better than before. They are found by Zhizhong Zeng, Kun He, Xinguo Yu, Wenqi Huang, Zhanghua Fu (their work is partly inspired by Tao Ye et el.) [30].
16-Jun-2015:	Some small improvements by rearrangements of circles for N=55, 56, 59, 68, 69, 72, 74, 75, 76, 78, 79, 81, 86, 87, 88, 90, 91, 93, 95, 96, 97, 98, 99 and 100 by Eckard Specht [31].
21-Oct-2015:	What a sensation! André Müller [33] found lots of new records, namely for N=52, 53, 55–59, 61–99, 101–199, which are not only a little bit better than the previous, but significantly better. It seems that all other people will have no chance to beat these results for years (except for small improvements by rearrangements). So, congratulation André, for these milestones!
01-Jun-2024:	Significant improvement for N= 40 by Jianrong Zhou, Jiyao He, and Kun He [33].
05-Jul-2026:	André Müller has published his records on github in December 2025 [32]. I could improve most of them only by a small amount.
24-Jul-2026:	Almost all of the new candidates, namely N=75–77, 82, 87, 90, 91, 93, 94, 100, 104, 106, 110, 112–121, 125, 127, 128, 130–137, 139, 140, 142–146, 148, 150, 153–155, 157, 158, 160, 162–178, 180–188, 190–200, 300, 400, 600, 800, 1000, 2000, could be slightly improved by simple swapping of circles [31]. But the credits should remain at the author.
25-Jul-2026:	I firmly believed that André's records would stand for a long time, but Wilfred Heap surprised today with really improved packings for 111(!) instances, namely for N=52, 53, 56, 58, 59, 61, 62, 64, 67, 68, 70–75, 77–89, 92, 94–99, 101–105, 107–111, 113–117, 119, 120, 122–126, 128–133, 135, 136, 138, 139–142, 144–150, 152, 155, 157, 160–166, 169, 171, 172, 174–179, 181–184, 186, 188–190, 192, 193, 195–198. Congratulations!
27-Jul-2026:	Almost all of the new candidates, namely N=56, 58, 61, 62, 64, 70–72, 74, 77–79, 82–85, 87, 88, 92, 94–97, 99, 101, 102, 104, 105, 107, 108, 110, 111, 113–117, 119, 120, 122–126, 128–133, 135, 136, 138–142, 144–150, 152, 155, 157, 160–166, 169, 171, 172, 174–179, 181–184, 186, 188–190, 192, 193, 195– 198, could be slightly improved by simple swapping of circles [31]. But the credits should remain at the author.

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[26]	, private communication, March 2011.
[27]	, private communication, January 2012–February 2013.
[28]	, private communication, March 2012.
[29]	, private communication, September 2012–March 2013.
[30]	Zhizhong Zeng, Kun He, Xinguo Yu, Wenqi Huang, Zhanghua Fu, private communication, July 2014.
[31]	, program ccin, 2005–2026.
[32]	, github.com/muellan/packing, December 2025.
[33]	, Solution-Hashing Search Based on Layout-Graph Transformation for Unequal Circle Packing, submitted to European Journal of Operational Research, under review, May 2024.
[34]	Eckard Specht, A precise algorithm to detect voids in polydisperse circle packings, Proc. R. Soc. A 471 (2015), 20150421.
[35]	, private communication, July 2026.

The best known packings of unequal circles with integer radii in a circle (complete up to N = 200)

Last update: 27-Jul-2026

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