Basic key method (most perfect)

In 2004 Donald Morris discovered (see website http://www.bestfranklinsquares.com/mcm2) the basic key method. The basic key is a 2 x n [n = multiple of 4] magic rectangle. You can use the method to construct magic squares which are a multiple of 4.

See the basic key to construct a 16x16 most perfect (Franklin pan)magic square:

1	2			3	4			5	6			7	8
		1	2			3	4			5	6			7	8

Take care that the sum of each column is the highest + lowest number from 1 up to 16 (16 + 1 =) 17.

1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8

Copy the two rows to fill the 16x16 square completely.

Column grid

1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8
1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8
1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8
1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8
1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8
1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8
1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8
1	2	16	15	3	4	14	13	5	6	12	11	7	8	10	9
16	15	1	2	14	13	3	4	12	11	5	6	10	9	7	8

Construct the second grid by rotating the first grid a quarter to the left.

Column grid

9	8	9	8	9	8	9	8	9	8	9	8	9	8	9	8
10	7	10	7	10	7	10	7	10	7	10	7	10	7	10	7
8	9	8	9	8	9	8	9	8	9	8	9	8	9	8	9
7	10	7	10	7	10	7	10	7	10	7	10	7	10	7	10
11	6	11	6	11	6	11	6	11	6	11	6	11	6	11	6
12	5	12	5	12	5	12	5	12	5	12	5	12	5	12	5
6	11	6	11	6	11	6	11	6	11	6	11	6	11	6	11
5	12	5	12	5	12	5	12	5	12	5	12	5	12	5	12
13	4	13	4	13	4	13	4	13	4	13	4	13	4	13	4
14	3	14	3	14	3	14	3	14	3	14	3	14	3	14	3
4	13	4	13	4	13	4	13	4	13	4	13	4	13	4	13
3	14	3	14	3	14	3	14	3	14	3	14	3	14	3	14
15	2	15	2	15	2	15	2	15	2	15	2	15	2	15	2
16	1	16	1	16	1	16	1	16	1	16	1	16	1	16	1
2	15	2	15	2	15	2	15	2	15	2	15	2	15	2	15
1	16	1	16	1	16	1	16	1	16	1	16	1	16	1	16

Take a number from the column grid and take the number of the same cell from the row grid and look it up in the table below.

		Column:	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16

Row:	1		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
	2		17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32
	3		33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48
	4		49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64
	5		65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80
	6		81	82	83	84	85	86	87	88	89	90	91	92	93	94	95	96
	7		97	98	99	100	101	102	103	104	105	106	107	108	109	110	111	112
	8		113	114	115	116	117	118	119	120	121	122	123	124	125	126	127	128
	9		129	130	131	132	133	134	135	136	137	138	139	140	141	142	143	144
	10		145	146	147	148	149	150	151	152	153	154	155	156	157	158	159	160
	11		161	162	163	164	165	166	167	168	169	170	171	172	173	174	175	176
	12		177	178	179	180	181	182	183	184	185	186	187	188	189	190	191	192
	13		193	194	195	196	197	198	199	200	201	202	203	204	205	206	207	208
	14		209	210	211	212	213	214	215	216	217	218	219	220	221	222	223	224
	15		225	226	227	228	229	230	231	232	233	234	235	236	237	238	239	240
	16		241	242	243	244	245	246	247	248	249	250	251	252	253	254	255	256

See below the result:

16x16 most perfect (Franklin pan)magic square

129	114	144	127	131	116	142	125	133	118	140	123	135	120	138	121
160	111	145	98	158	109	147	100	156	107	149	102	154	105	151	104
113	130	128	143	115	132	126	141	117	134	124	139	119	136	122	137
112	159	97	146	110	157	99	148	108	155	101	150	106	153	103	152
161	82	176	95	163	84	174	93	165	86	172	91	167	88	170	89
192	79	177	66	190	77	179	68	188	75	181	70	186	73	183	72
81	162	96	175	83	164	94	173	85	166	92	171	87	168	90	169
80	191	65	178	78	189	67	180	76	187	69	182	74	185	71	184
193	50	208	63	195	52	206	61	197	54	204	59	199	56	202	57