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