Basic pattern method (1) a
Use 36x the same panmagic 4x4 square and 2 fixed grids to construct a most perfect (Franklin pan)magic 24x24 square.
Take 1x number from grid with 36x the same panmagic 4x4 square
| 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 |
| 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 |
| 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 |
| 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 |
| 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 |
| 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 |
| 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 |
| 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 |
| 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 |
| 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 |
| 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 |
| 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 |
| 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 |
| 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 |
| 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 |
| 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 |
| 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 |
| 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 |
| 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 |
| 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 |
| 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 | 15 | 6 | 12 | 1 |
| 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 | 4 | 9 | 7 | 14 |
| 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 | 5 | 16 | 2 | 11 |
| 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 | 10 | 3 | 13 | 8 |
+ 16x number from first fixed grid
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
| 0 | 5 | 5 | 0 | 5 | 0 | 0 | 5 | 1 | 4 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 3 | 2 | 2 | 3 |
| 5 | 0 | 0 | 5 | 0 | 5 | 5 | 0 | 4 | 1 | 1 | 4 | 1 | 4 | 4 | 1 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 2 |
+ 96x number from second fixed grid
| 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 |
| 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 |
| 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 |
| 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 |
| 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 |
| 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 |
| 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 |
| 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 |
| 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 |
| 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 |
| 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 |
| 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 |
| 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 |
| 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 |
| 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 |
| 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 | 4 | 1 |
| 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 |
| 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 |
| 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 |
| 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 |
| 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 |
| 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 |
| 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 |
| 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 2 |
= 24x24 most perfect (Franklin pan)magic square
| 15 | 566 | 92 | 481 | 95 | 486 | 12 | 561 | 31 | 550 | 76 | 497 | 79 | 502 | 28 | 545 | 47 | 534 | 60 | 513 | 63 | 518 | 44 | 529 |
| 564 | 9 | 487 | 94 | 484 | 89 | 567 | 14 | 548 | 25 | 503 | 78 | 500 | 73 | 551 | 30 | 532 | 41 | 519 | 62 | 516 | 57 | 535 | 46 |
| 485 | 96 | 562 | 11 | 565 | 16 | 482 | 91 | 501 | 80 | 546 | 27 | 549 | 32 | 498 | 75 | 517 | 64 | 530 | 43 | 533 | 48 | 514 | 59 |
| 90 | 483 | 13 | 568 | 10 | 563 | 93 | 488 | 74 | 499 | 29 | 552 | 26 | 547 | 77 | 504 | 58 | 515 | 45 | 536 | 42 | 531 | 61 | 520 |
| 495 | 86 | 572 | 1 | 575 | 6 | 492 | 81 | 511 | 70 | 556 | 17 | 559 | 22 | 508 | 65 | 527 | 54 | 540 | 33 | 543 | 38 | 524 | 49 |
| 84 | 489 | 7 | 574 | 4 | 569 | 87 | 494 | 68 | 505 | 23 | 558 | 20 | 553 | 71 | 510 | 52 | 521 | 39 | 542 | 36 | 537 | 55 | 526 |
| 5 | 576 | 82 | 491 | 85 | 496 | 2 | 571 | 21 | 560 | 66 | 507 | 69 | 512 | 18 | 555 | 37 | 544 | 50 | 523 | 53 | 528 | 34 | 539 |
| 570 | 3 | 493 | 88 | 490 | 83 | 573 | 8 | 554 | 19 | 509 | 72 | 506 | 67 | 557 | 24 | 538 | 35 | 525 | 56 | 522 | 51 | 541 | 40 |
| 111 | 470 | 188 | 385 | 191 | 390 | 108 | 465 | 127 | 454 | 172 | 401 | 175 | 406 | 124 | 449 | 143 | 438 | 156 | 417 | 159 | 422 | 140 | 433 |
| 468 | 105 | 391 | 190 | 388 | 185 | 471 | 110 | 452 | 121 | 407 | 174 | 404 | 169 | 455 | 126 | 436 | 137 | 423 | 158 | 420 | 153 | 439 | 142 |
| 389 | 192 | 466 | 107 | 469 | 112 | 386 | 187 | 405 | 176 | 450 | 123 | 453 | 128 | 402 | 171 | 421 | 160 | 434 | 139 | 437 | 144 | 418 | 155 |
| 186 | 387 | 109 | 472 | 106 | 467 | 189 | 392 | 170 | 403 | 125 | 456 | 122 | 451 | 173 | 408 | 154 | 419 | 141 | 440 | 138 | 435 | 157 | 424 |
| 399 | 182 | 476 | 97 | 479 | 102 | 396 | 177 | 415 | 166 | 460 | 113 | 463 | 118 | 412 | 161 | 431 | 150 | 444 | 129 | 447 | 134 | 428 | 145 |
| 180 | 393 | 103 | 478 | 100 | 473 | 183 | 398 | 164 | 409 | 119 | 462 | 116 | 457 | 167 | 414 | 148 | 425 | 135 | 446 | 132 | 441 | 151 | 430 |
| 101 | 480 | 178 | 395 | 181 | 400 | 98 | 475 | 117 | 464 | 162 | 411 | 165 | 416 | 114 | 459 | 133 | 448 | 146 | 427 | 149 | 432 | 130 | 443 |
| 474 | 99 | 397 | 184 | 394 | 179 | 477 | 104 | 458 | 115 | 413 | 168 | 410 | 163 | 461 | 120 | 442 | 131 | 429 | 152 | 426 | 147 | 445 | 136 |
| 207 | 374 | 284 | 289 | 287 | 294 | 204 | 369 | 223 | 358 | 268 | 305 | 271 | 310 | 220 | 353 | 239 | 342 | 252 | 321 | 255 | 326 | 236 | 337 |
| 372 | 201 | 295 | 286 | 292 | 281 | 375 | 206 | 356 | 217 | 311 | 270 | 308 | 265 | 359 | 222 | 340 | 233 | 327 | 254 | 324 | 249 | 343 | 238 |
| 293 | 288 | 370 | 203 | 373 | 208 | 290 | 283 | 309 | 272 | 354 | 219 | 357 | 224 | 306 | 267 | 325 | 256 | 338 | 235 | 341 | 240 | 322 | 251 |
| 282 | 291 | 205 | 376 | 202 | 371 | 285 | 296 | 266 | 307 | 221 | 360 | 218 | 355 | 269 | 312 | 250 | 323 | 237 | 344 | 234 | 339 | 253 | 328 |
| 303 | 278 | 380 | 193 | 383 | 198 | 300 | 273 | 319 | 262 | 364 | 209 | 367 | 214 | 316 | 257 | 335 | 246 | 348 | 225 | 351 | 230 | 332 | 241 |
| 276 | 297 | 199 | 382 | 196 | 377 | 279 | 302 | 260 | 313 | 215 | 366 | 212 | 361 | 263 | 318 | 244 | 329 | 231 | 350 | 228 | 345 | 247 | 334 |
| 197 | 384 | 274 | 299 | 277 | 304 | 194 | 379 | 213 | 368 | 258 | 315 | 261 | 320 | 210 | 363 | 229 | 352 | 242 | 331 | 245 | 336 | 226 | 347 |
| 378 | 195 | 301 | 280 | 298 | 275 | 381 | 200 | 362 | 211 | 317 | 264 | 314 | 259 | 365 | 216 | 346 | 227 | 333 | 248 | 330 | 243 | 349 | 232 |
Notify that this 24x24 magic square has the extra tight Willem Barink structure.
Use basic pattern method (1) to construct magic squares of order is multiple of 4 from 8x8 to infinity. See 8x8, 12x12, 16x16a, 16x16b, 16x16c, 20x20, 24x24a, 24x24b, 28x28, 32x32a, 32x32b, 32x32c and 32x32d
