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