These designs are derived from sub-groups of the multiplicative subgroups of doubly homogeneous groups.
| v | b | r | First Initial block | Multiplied by:- |
|---|---|---|---|---|
| 43 | 43 | 21 | (1,36,6 | 9,23,11 | 38,35,13 | 41,14,31 | 25,40,21 | 10,16,17 | 4,15,24) | 1 mod 43 |
| 127 | 381 | 63 | (1,107,19 | 94,25,8 | 73,64,117 | 4,47,76 | 122,100,32 | 38,2,87 | 16,61,50) | 1, 9, 81,...,81 mod 127 |
| 211 | 1055 | 105 | (1,196,14 | 180,43,199 | 117,144,161 | 171,178,73 | 185,179,58 | 173,148,101 | 123,54,34) | 1, 4, 16,...,45 mod 211 |
| 379 | 3411 | 189 | (1,327,51 | 255,5,119 | 216,138,25 | 125,322,311 | 39,246,94 | 91,195,93 | 86,76,217) | 1, 4, 16,...,348 mod 379 |
| 463 | 5093 | 231 | (1,21,441 | 251,178,34 | 33,230,200 | 412,318,196 | 163,182,118 | 169,308,449 | 286,450,190) | 1, 9, 81,...,388 mod 463 |
| 547 | 7111 | 273 | (1,40,506 | 169,196,182 | 117,304,126 | 81,505,508 | 14,13,520 | 178,9,360 | 544,427,123) | 1, 4, 16,...,179 mod 547 |
| 631 | 9465 | 315 | (1,587,43 | 458,40,133 | 272,21,338 | 269,153,209 | 157,33,441 | 603,601,58 | 427,142,62) | 1, 9, 81,...,121 mod 631 |
| 883 | 18543 | 441 | (1,545,337 | 729,838,199 | 758,749,259 | 707,327,732 | 614,856,296 | 808,626,332 | 71,726,86) | 1, 4, 16,...,403 mod 883 |
| 967 | 22241 | 483 | (1,824,142 | 577,651,706 | 281,431,255 | 648,168,151 | 634,236,97 | 292,792,850 | 226,560,181) | 1, 25, 625,...,758 mod 967 |
| 1051 | 26275 | 525 | (1,870,180 | 464,96,491 | 892,402,808 | 845,501,756 | 57,193,801 | 173,217,661 | 396,843,863) | 1, 49, 299,...,417 mod 1051 |
| 1303 | 40393 | 651 | (1,1207,95 | 1016,189,98 | 280,483,540 | 426,800,77 | 220,1031,52 | 707,1187,712 | 359,717,227) | 1, 36, 1296,...,173 mod 1303 |
| 1471 | 51485 | 735 | (1,1219,251 | 765,1392,785 | 1238,1347,357 | 1217,755,970 | 1333,943,666 | 342,605,524 | 1263,931,748) | 1, 36, 1296,...,389 mod 1471 |
| 1723 | 70643 | 861 | (1,1681,41 | 677,857,189 | 11,1261,451 | 555,812,356 | 121,87,1515 | 936,317,470 | 1331,957,1158) | 1, 9, 81,...,841 mod 1723 |
| 2143 | 109293 | 1071 | (1,1793,349 | 1818,171,154 | 618,143,1382 | 592,671,880 | 470,511,1162 | 1546,1079,1661 | 1155,777,211) | 1, 9, 81,...,202 mod 2143 |
| 2311 | 127105 | 1155 | (1,1428,882 | 574,1578,159 | 1314,2171,1137 | 850,525,936 | 279,920,1112 | 687,1172,452 | 1468,227,616) | 1, 9, 81,...,2118 mod 2311 |
| 2647 | 166761 | 1323 | (1,185,2461 | 453,1748,446 | 1390,391,866 | 2331,2421,542 | 2437,855,2002 | 162,853,1632 | 1917,2594,783) | 1, 9, 81,...,1815 mod 2647 |
| 2731 | 177515 | 1365 | (1,2284,446 | 2103,2154,1205 | 1120,1864,2478 | 1238,1007,486 | 871,1196,664 | 1943,2668,851 | 553,1330,848) | 1, 9, 81,...,1144 mod 2731 |
| 3067 | 223891 | 1533 | (1,2093,973 | 2455,1090,2589 | 370,1526,1171 | 518,1523,1026 | 1952,292,823 | 1506,2249,2379 | 1495,695,877) | 1, 4, 16,...,2914 mod 3067 |
| 3319 | 262201 | 1659 | (1,1527,1791 | 1313,275,1731 | 1408,2623,2607 | 21,2196,1102 | 1021,2456,3161 | 3016,1979,1643 | 441,2969,3228) | 1, 36, 1296,...,1235 mod 3319 |
| 3571 | 303535 | 1785 | (1,3467,103 | 2141,2309,2692 | 2288,1305,3549 | 2767,1483,2892 | 3429,484,3229 | 3084,654,3404 | 65,382,3124) | 1, 4, 16,...,1428 mod 3571 |
| 3739 | 332771 | 1869 | (1,3044,694 | 85,749,2905 | 3486,102,151 | 929,1192,1618 | 446,367,2926 | 520,1283,1936 | 3071,624,44) | 1, 49, 2401,...,2062 mod 3739 |
| 3823 | 347893 | 1911 | (1,2638,1184 | 3328,1656,2662 | 353,2225,1245 | 1123,3472,3051 | 2273,1710,3663 | 2650,2256,2740 | 3362,3419,865) | 1, 9, 81,...,3768 mod 3823 |
| 3907 | 363351 | 1953 | (1,3844,62 | 2488,3443,1883 | 1456,2040,411 | 739,327,2841 | 2342,920,645 | 1559,3365,2890 | 3048,3326,1440) | 1, 4, 16,...,622 mod 3907 |
| 4159 | 411741 | 2079 | (1,1604,2554 | 1233,2207,719 | 2254,1245,660 | 970,414,2775 | 2377,3064,2877 | 2905,1540,3873 | 966,2316,877) | 1, 9, 81,...,137 mod 4159 |
| 4243 | 428543 | 2121 | (1,298,3944 | 2194,390,1659 | 2074,2817,3595 | 1860,2690,3936 | 3317,4090,1079 | 753,3758,3975 | 1555,903,1785) | 1, 4, 16,...,2670 mod 4243 |