These designs are derived from sub-groups of the multiplicative subgroups of doubly homogeneous groups.
| v | b | r | First Initial block | Multiplied by:- |
|---|---|---|---|---|
| 31 | 31 | 15 | (1,25,5 | 9,8,14 | 19,10,2 | 16,28,18 | 20,4,7) | 1 mod 31 |
| 151 | 755 | 75 | (1,32,118 | 38,8,105 | 85,2,64 | 59,76,16 | 128,19,4) | 1, 36, 88,...,43 mod 151 |
| 211 | 1477 | 105 | (1,196,14 | 137,55,19 | 201,150,71 | 107,83,21 | 100,188,134) | 1, 4, 16,...,87 mod 211 |
| 271 | 2439 | 135 | (1,242,28 | 90,100,81 | 241,57,244 | 10,252,9 | 87,187,268) | 1, 36, 212,...,138 mod 271 |
| 331 | 3641 | 165 | (1,299,31 | 203,124,4 | 165,16,150 | 64,269,329 | 83,323,256) | 1, 9, 81,...,280 mod 331 |
| 571 | 10849 | 285 | (1,109,461 | 331,106,134 | 500,255,387 | 481,468,193 | 473,167,502) | 1, 9, 81,...,354 mod 571 |
| 631 | 13251 | 315 | (1,587,43 | 562,512,188 | 344,8,279 | 242,79,310 | 339,228,64) | 1, 9, 81,...,413 mod 631 |
| 691 | 15893 | 345 | (1,437,253 | 383,149,159 | 197,405,89 | 132,331,228 | 113,320,258) | 1, 9, 81,...,580 mod 691 |
| 751 | 18775 | 375 | (1,678,72 | 437,392,673 | 215,76,460 | 80,168,503 | 414,569,519) | 1, 9, 81,...,132 mod 751 |
| 811 | 21897 | 405 | (1,680,130 | 276,339,196 | 753,299,570 | 212,613,797 | 120,500,191) | 1, 9, 81,...,301 mod 811 |
| 991 | 32703 | 495 | (1,113,877 | 86,799,106 | 459,335,197 | 825,71,95 | 589,160,242) | 1, 36, 305,...,608 mod 991 |
| 1051 | 36785 | 525 | (1,870,180 | 608,307,136 | 763,629,710 | 413,919,770 | 966,671,465) | 1, 49, 299,...,184 mod 1051 |
| 1171 | 45669 | 585 | (1,420,750 | 402,216,553 | 6,178,987 | 70,125,976 | 36,1068,67) | 1, 4, 16,...,686 mod 1171 |
| 1231 | 50471 | 615 | (1,126,1104 | 563,771,1128 | 602,761,1099 | 401,55,775 | 490,190,551) | 1, 9, 81,...,1020 mod 1231 |
| 1291 | 55513 | 645 | (1,346,944 | 245,855,191 | 639,333,319 | 344,252,695 | 365,1063,1154) | 1, 4, 16,...,384 mod 1291 |
| 1471 | 72079 | 735 | (1,1219,251 | 998,45,428 | 137,780,554 | 1394,281,1267 | 1117,948,877) | 1, 36, 1296,...,1417 mod 1471 |
| 1531 | 78081 | 765 | (1,884,646 | 59,102,1370 | 419,1425,1218 | 225,1401,1436 | 1027,1516,519) | 1, 4, 16,...,1163 mod 1531 |
| 1831 | 111691 | 915 | (1,1158,672 | 261,123,1447 | 374,976,481 | 571,227,1033 | 720,655,456) | 1, 9, 81,...,29 mod 1831 |
| 1951 | 126815 | 975 | (1,76,1874 | 320,908,723 | 948,1812,1142 | 955,393,603 | 1244,896,1762) | 1, 9, 81,...,1553 mod 1951 |
| 2011 | 134737 | 1005 | (1,205,1805 | 912,1948,1162 | 1201,863,1958 | 1328,755,1939 | 514,798,699) | 1, 9, 81,...,1442 mod 2011 |
| 2131 | 151301 | 1065 | (1,468,1662 | 1507,2046,709 | 1534,1896,832 | 1734,1732,796 | 532,1780,1950) | 1, 4, 16,...,1975 mod 2131 |
| 2251 | 168825 | 1125 | (1,708,1542 | 871,2145,1486 | 54,2216,2232 | 2014,1029,1459 | 665,361,1225) | 1, 49, 150,...,1350 mod 2251 |
| 2311 | 177947 | 1155 | (1,1428,882 | 429,197,1685 | 1472,1317,1833 | 585,1109,617 | 1377,2006,1239) | 1, 9, 81,...,818 mod 2311 |
| 2371 | 187309 | 1185 | (1,464,1906 | 483,1238,650 | 931,462,978 | 1554,272,545 | 1346,971,54) | 1, 4, 16,...,1899 mod 2371 |
| 2551 | 216835 | 1275 | (1,50,2500 | 376,943,1232 | 1071,2530,1501 | 2189,2308,605 | 1642,468,441) | 1, 36, 1296,...,2278 mod 2551 |
| 2671 | 237719 | 1335 | (1,2126,544 | 1775,2198,1369 | 1516,1790,2036 | 1203,1431,37 | 1196,2575,1571) | 1, 49, 2401,...,1508 mod 2671 |
| 2731 | 248521 | 1365 | (1,2284,446 | 987,1233,511 | 1933,1676,1853 | 1633,1957,1872 | 481,742,1508) | 1, 9, 81,...,1020 mod 2731 |
| 2791 | 259563 | 1395 | (1,91,2699 | 1727,861,203 | 1741,2135,1706 | 800,234,1757 | 55,2214,522) | 1, 36, 1296,...,1521 mod 2791 |
| 2851 | 270845 | 1425 | (1,1014,1836 | 2792,45,14 | 630,196,2025 | 2744,2691,267 | 611,887,1353) | 1, 4, 16,...,698 mod 2851 |
| 2971 | 294129 | 1485 | (1,2916,54 | 1117,956,898 | 2840,1263,1839 | 2223,2517,1202 | 2306,923,2713) | 1, 100, 1087,...,2180 mod 2971 |