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To find new construction methods you must analyze magic squares.
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I have splitted a (most perfect) Franklin panmagic 32x32 square in grids with 4x4 Sudoku sub-squares.
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32x32 (most perfect) Franklin panmagic square
15 | 1014 | 124 | 897 | 127 | 902 | 12 | 1009 | 31 | 998 | 108 | 913 | 111 | 918 | 28 | 993 | 47 | 982 | 92 | 929 | 95 | 934 | 44 | 977 | 63 | 966 | 76 | 945 | 79 | 950 | 60 | 961 |
1012 | 9 | 903 | 126 | 900 | 121 | 1015 | 14 | 996 | 25 | 919 | 110 | 916 | 105 | 999 | 30 | 980 | 41 | 935 | 94 | 932 | 89 | 983 | 46 | 964 | 57 | 951 | 78 | 948 | 73 | 967 | 62 |
901 | 128 | 1010 | 11 | 1013 | 16 | 898 | 123 | 917 | 112 | 994 | 27 | 997 | 32 | 914 | 107 | 933 | 96 | 978 | 43 | 981 | 48 | 930 | 91 | 949 | 80 | 962 | 59 | 965 | 64 | 946 | 75 |
122 | 899 | 13 | 1016 | 10 | 1011 | 125 | 904 | 106 | 915 | 29 | 1000 | 26 | 995 | 109 | 920 | 90 | 931 | 45 | 984 | 42 | 979 | 93 | 936 | 74 | 947 | 61 | 968 | 58 | 963 | 77 | 952 |
911 | 118 | 1020 | 1 | 1023 | 6 | 908 | 113 | 927 | 102 | 1004 | 17 | 1007 | 22 | 924 | 97 | 943 | 86 | 988 | 33 | 991 | 38 | 940 | 81 | 959 | 70 | 972 | 49 | 975 | 54 | 956 | 65 |
116 | 905 | 7 | 1022 | 4 | 1017 | 119 | 910 | 100 | 921 | 23 | 1006 | 20 | 1001 | 103 | 926 | 84 | 937 | 39 | 990 | 36 | 985 | 87 | 942 | 68 | 953 | 55 | 974 | 52 | 969 | 71 | 958 |
5 | 1024 | 114 | 907 | 117 | 912 | 2 | 1019 | 21 | 1008 | 98 | 923 | 101 | 928 | 18 | 1003 | 37 | 992 | 82 | 939 | 85 | 944 | 34 | 987 | 53 | 976 | 66 | 955 | 69 | 960 | 50 | 971 |
1018 | 3 | 909 | 120 | 906 | 115 | 1021 | 8 | 1002 | 19 | 925 | 104 | 922 | 99 | 1005 | 24 | 986 | 35 | 941 | 88 | 938 | 83 | 989 | 40 | 970 | 51 | 957 | 72 | 954 | 67 | 973 | 56 |
143 | 886 | 252 | 769 | 255 | 774 | 140 | 881 | 159 | 870 | 236 | 785 | 239 | 790 | 156 | 865 | 175 | 854 | 220 | 801 | 223 | 806 | 172 | 849 | 191 | 838 | 204 | 817 | 207 | 822 | 188 | 833 |
884 | 137 | 775 | 254 | 772 | 249 | 887 | 142 | 868 | 153 | 791 | 238 | 788 | 233 | 871 | 158 | 852 | 169 | 807 | 222 | 804 | 217 | 855 | 174 | 836 | 185 | 823 | 206 | 820 | 201 | 839 | 190 |
773 | 256 | 882 | 139 | 885 | 144 | 770 | 251 | 789 | 240 | 866 | 155 | 869 | 160 | 786 | 235 | 805 | 224 | 850 | 171 | 853 | 176 | 802 | 219 | 821 | 208 | 834 | 187 | 837 | 192 | 818 | 203 |
250 | 771 | 141 | 888 | 138 | 883 | 253 | 776 | 234 | 787 | 157 | 872 | 154 | 867 | 237 | 792 | 218 | 803 | 173 | 856 | 170 | 851 | 221 | 808 | 202 | 819 | 189 | 840 | 186 | 835 | 205 | 824 |
783 | 246 | 892 | 129 | 895 | 134 | 780 | 241 | 799 | 230 | 876 | 145 | 879 | 150 | 796 | 225 | 815 | 214 | 860 | 161 | 863 | 166 | 812 | 209 | 831 | 198 | 844 | 177 | 847 | 182 | 828 | 193 |
244 | 777 | 135 | 894 | 132 | 889 | 247 | 782 | 228 | 793 | 151 | 878 | 148 | 873 | 231 | 798 | 212 | 809 | 167 | 862 | 164 | 857 | 215 | 814 | 196 | 825 | 183 | 846 | 180 | 841 | 199 | 830 |
133 | 896 | 242 | 779 | 245 | 784 | 130 | 891 | 149 | 880 | 226 | 795 | 229 | 800 | 146 | 875 | 165 | 864 | 210 | 811 | 213 | 816 | 162 | 859 | 181 | 848 | 194 | 827 | 197 | 832 | 178 | 843 |
890 | 131 | 781 | 248 | 778 | 243 | 893 | 136 | 874 | 147 | 797 | 232 | 794 | 227 | 877 | 152 | 858 | 163 | 813 | 216 | 810 | 211 | 861 | 168 | 842 | 179 | 829 | 200 | 826 | 195 | 845 | 184 |
271 | 758 | 380 | 641 | 383 | 646 | 268 | 753 | 287 | 742 | 364 | 657 | 367 | 662 | 284 | 737 | 303 | 726 | 348 | 673 | 351 | 678 | 300 | 721 | 319 | 710 | 332 | 689 | 335 | 694 | 316 | 705 |
756 | 265 | 647 | 382 | 644 | 377 | 759 | 270 | 740 | 281 | 663 | 366 | 660 | 361 | 743 | 286 | 724 | 297 | 679 | 350 | 676 | 345 | 727 | 302 | 708 | 313 | 695 | 334 | 692 | 329 | 711 | 318 |
645 | 384 | 754 | 267 | 757 | 272 | 642 | 379 | 661 | 368 | 738 | 283 | 741 | 288 | 658 | 363 | 677 | 352 | 722 | 299 | 725 | 304 | 674 | 347 | 693 | 336 | 706 | 315 | 709 | 320 | 690 | 331 |
378 | 643 | 269 | 760 | 266 | 755 | 381 | 648 | 362 | 659 | 285 | 744 | 282 | 739 | 365 | 664 | 346 | 675 | 301 | 728 | 298 | 723 | 349 | 680 | 330 | 691 | 317 | 712 | 314 | 707 | 333 | 696 |
655 | 374 | 764 | 257 | 767 | 262 | 652 | 369 | 671 | 358 | 748 | 273 | 751 | 278 | 668 | 353 | 687 | 342 | 732 | 289 | 735 | 294 | 684 | 337 | 703 | 326 | 716 | 305 | 719 | 310 | 700 | 321 |
372 | 649 | 263 | 766 | 260 | 761 | 375 | 654 | 356 | 665 | 279 | 750 | 276 | 745 | 359 | 670 | 340 | 681 | 295 | 734 | 292 | 729 | 343 | 686 | 324 | 697 | 311 | 718 | 308 | 713 | 327 | 702 |
261 | 768 | 370 | 651 | 373 | 656 | 258 | 763 | 277 | 752 | 354 | 667 | 357 | 672 | 274 | 747 | 293 | 736 | 338 | 683 | 341 | 688 | 290 | 731 | 309 | 720 | 322 | 699 | 325 | 704 | 306 | 715 |
762 | 259 | 653 | 376 | 650 | 371 | 765 | 264 | 746 | 275 | 669 | 360 | 666 | 355 | 749 | 280 | 730 | 291 | 685 | 344 | 682 | 339 | 733 | 296 | 714 | 307 | 701 | 328 | 698 | 323 | 717 | 312 |
399 | 630 | 508 | 513 | 511 | 518 | 396 | 625 | 415 | 614 | 492 | 529 | 495 | 534 | 412 | 609 | 431 | 598 | 476 | 545 | 479 | 550 | 428 | 593 | 447 | 582 | 460 | 561 | 463 | 566 | 444 | 577 |
628 | 393 | 519 | 510 | 516 | 505 | 631 | 398 | 612 | 409 | 535 | 494 | 532 | 489 | 615 | 414 | 596 | 425 | 551 | 478 | 548 | 473 | 599 | 430 | 580 | 441 | 567 | 462 | 564 | 457 | 583 | 446 |
517 | 512 | 626 | 395 | 629 | 400 | 514 | 507 | 533 | 496 | 610 | 411 | 613 | 416 | 530 | 491 | 549 | 480 | 594 | 427 | 597 | 432 | 546 | 475 | 565 | 464 | 578 | 443 | 581 | 448 | 562 | 459 |
506 | 515 | 397 | 632 | 394 | 627 | 509 | 520 | 490 | 531 | 413 | 616 | 410 | 611 | 493 | 536 | 474 | 547 | 429 | 600 | 426 | 595 | 477 | 552 | 458 | 563 | 445 | 584 | 442 | 579 | 461 | 568 |
527 | 502 | 636 | 385 | 639 | 390 | 524 | 497 | 543 | 486 | 620 | 401 | 623 | 406 | 540 | 481 | 559 | 470 | 604 | 417 | 607 | 422 | 556 | 465 | 575 | 454 | 588 | 433 | 591 | 438 | 572 | 449 |
500 | 521 | 391 | 638 | 388 | 633 | 503 | 526 | 484 | 537 | 407 | 622 | 404 | 617 | 487 | 542 | 468 | 553 | 423 | 606 | 420 | 601 | 471 | 558 | 452 | 569 | 439 | 590 | 436 | 585 | 455 | 574 |
389 | 640 | 498 | 523 | 501 | 528 | 386 | 635 | 405 | 624 | 482 | 539 | 485 | 544 | 402 | 619 | 421 | 608 | 466 | 555 | 469 | 560 | 418 | 603 | 437 | 592 | 450 | 571 | 453 | 576 | 434 | 587 |
634 | 387 | 525 | 504 | 522 | 499 | 637 | 392 | 618 | 403 | 541 | 488 | 538 | 483 | 621 | 408 | 602 | 419 | 557 | 472 | 554 | 467 | 605 | 424 | 586 | 435 | 573 | 456 | 570 | 451 | 589 | 440 |
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First grid (number +1)
2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 |
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Second grid (number x 4)
3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 |
0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 |
1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 |
2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 |
3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 |
0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 |
1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 |
2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 |
3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 |
0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 |
1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 |
2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 |
3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 | 3 | 1 | 2 | 0 |
0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 | 0 | 2 | 1 | 3 |
1 | 3 | 0 |