Use 4x4 the same 4x4 Sudoku pattern (as first grid) and a second fixed grid to construct a most perfect magic 16x16 square.
Take 1x number from first grid +1
2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 |
3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 |
0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 |
1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 |
2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 |
3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 |
0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 |
1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 |
2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 |
3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 |
0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 |
1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 |
2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 |
3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 |
0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 |
1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 |
+ 4x number from second grid
63 | 7 | 56 | 0 | 62 | 6 | 57 | 1 | 61 | 5 | 58 | 2 | 60 | 4 | 59 | 3 |
0 | 56 | 7 | 63 | 1 | 57 | 6 | 62 | 2 | 58 | 5 | 61 | 3 | 59 | 4 | 60 |
7 | 63 | 0 | 56 | 6 | 62 | 1 | 57 | 5 | 61 | 2 | 58 | 4 | 60 | 3 | 59 |
56 | 0 | 63 | 7 | 57 | 1 | 62 | 6 | 58 | 2 | 61 | 5 | 59 | 3 | 60 | 4 |
55 | 15 | 48 | 8 | 54 | 14 | 49 | 9 | 53 | 13 | 50 | 10 | 52 | 12 | 51 | 11 |
8 | 48 | 15 | 55 | 9 | 49 | 14 | 54 | 10 | 50 | 13 | 53 | 11 | 51 | 12 | 52 |
15 | 55 | 8 | 48 | 14 | 54 | 9 | 49 | 13 | 53 | 10 | 50 | 12 | 52 | 11 | 51 |
48 | 8 | 55 | 15 | 49 | 9 | 54 | 14 | 50 | 10 | 53 | 13 | 51 | 11 | 52 | 12 |
47 | 23 | 40 | 16 | 46 | 22 | 41 | 17 | 45 | 21 | 42 | 18 | 44 | 20 | 43 | 19 |
16 | 40 | 23 | 47 | 17 | 41 | 22 | 46 | 18 | 42 | 21 | 45 | 19 | 43 | 20 | 44 |
23 | 47 | 16 | 40 | 22 | 46 | 17 | 41 | 21 | 45 | 18 | 42 | 20 | 44 | 19 | 43 |
40 | 16 | 47 | 23 | 41 | 17 | 46 | 22 | 42 | 18 | 45 | 21 | 43 | 19 | 44 | 20 |
39 | 31 | 32 | 24 | 38 | 30 | 33 | 25 | 37 | 29 | 34 | 26 | 36 | 28 | 35 | 27 |
24 | 32 | 31 | 39 | 25 | 33 | 30 | 38 | 26 | 34 | 29 | 37 | 27 | 35 | 28 | 36 |
31 | 39 | 24 | 32 | 30 | 38 | 25 | 33 | 29 | 37 | 26 | 34 | 28 | 36 | 27 | 35 |
32 | 24 | 39 | 31 | 33 | 25 | 38 | 30 | 34 | 26 | 37 | 29 | 35 | 27 | 36 | 28 |
= 16x16 most perfect (Franklin pan)magic square
255 | 30 | 228 | 1 | 251 | 26 | 232 | 5 | 247 | 22 | 236 | 9 | 243 | 18 | 240 | 13 |
4 | 225 | 31 | 254 | 8 | 229 | 27 | 250 | 12 | 233 | 23 | 246 | 16 | 237 | 19 | 242 |
29 | 256 | 2 | 227 | 25 | 252 | 6 | 231 | 21 | 248 | 10 | 235 | 17 | 244 | 14 | 239 |
226 | 3 | 253 | 32 | 230 | 7 | 249 | 28 | 234 | 11 | 245 | 24 | 238 | 15 | 241 | 20 |
223 | 62 | 196 | 33 | 219 | 58 | 200 | 37 | 215 | 54 | 204 | 41 | 211 | 50 | 208 | 45 |
36 | 193 | 63 | 222 | 40 | 197 | 59 | 218 | 44 | 201 | 55 | 214 | 48 | 205 | 51 | 210 |
61 | 224 | 34 | 195 | 57 | 220 | 38 | 199 | 53 | 216 | 42 | 203 | 49 | 212 | 46 | 207 |
194 | 35 | 221 | 64 | 198 | 39 | 217 | 60 | 202 | 43 | 213 | 56 | 206 | 47 | 209 | 52 |
191 | 94 | 164 | 65 | 187 | 90 | 168 | 69 | 183 | 86 | 172 | 73 | 179 | 82 | 176 | 77 |
68 | 161 | 95 | 190 | 72 | 165 | 91 | 186 | 76 | 169 | 87 | 182 | 80 | 173 | 83 | 178 |
93 | 192 | 66 | 163 | 89 | 188 | 70 | 167 | 85 | 184 | 74 | 171 | 81 | 180 | 78 | 175 |
162 | 67 | 189 | 96 | 166 | 71 | 185 | 92 | 170 | 75 | 181 | 88 | 174 | 79 | 177 | 84 |
159 | 126 | 132 | 97 | 155 | 122 | 136 | 101 | 151 | 118 | 140 | 105 | 147 | 114 | 144 | 109 |
100 | 129 | 127 | 158 | 104 | 133 | 123 | 154 | 108 | 137 | 119 | 150 | 112 | 141 | 115 | 146 |
125 | 160 | 98 | 131 | 121 | 156 | 102 | 135 | 117 | 152 | 106 | 139 | 113 | 148 | 110 | 143 |
130 | 99 | 157 | 128 | 134 | 103 | 153 | 124 | 138 | 107 | 149 | 120 | 142 | 111 | 145 | 116 |
Use this method to construct most perfect (Franklin pan)magic squares which are a multiple of 4 from 8x8 to infinite. See
8x8, 12x12, 16x16, 20x20, 24x24, 28x28 and 32x32