The tables below give the best lower bounds on the sizes of difference triangle sets known. Following each entry is a pointer to the appropriate reference in the list below the table. References are generally the first (known to me) to prove a particular bound. Values known to be optimal are linked to the appropriate place in a separate list of optimal difference triangle sets.
Last update May 17, 2004.
J\I | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
1 | 1 T | 2 T | 3 T | 4 T | 5 T | 6 T | 7 T | 8 T |
2 | 3 T | 7 F | 10 F | 12 T | 15 T | 19 F | 22 F | 24 T |
3 | 6 T | 13 RB | 19 RB | 24 T | 30 T | 36 T | 42 T | 48 T |
4 | 11 RB | 22 RB | 32 GM | 41 GM | 51 F | 60 T | 71 F | 80 T |
5 | 17 RB | 34 GM | 49 GM | 64 JS2 | 79 JS5 | 92 JS5 | 108 JS5 | 123 JS5 |
6 | 25 RB | 51 GM | 72 JS2 | 94 JS3 | 113 JS5 | 136 JS5 | 158 JS5 | 181 JS5 |
7 | 34 WM | 70 JS2 | 100 JS5 | 124 JS5 | 155 JS5 | 186 JS5 | 217 JS5 | 247 JS5 |
8 | 44 WM | 94 JS2 | 124 JS5 | 164 JS5 | 205 JS5 | 245 JS5 | 286 JS5 | 327 JS5 |
9 | 55 WM | 121 JS5 | 158 JS5 | 209 JS5 | 261 JS5 | 313 JS5 | 365 JS5 | 417 JS5 |
10 | 72 WM | 132 JS5 | 197 JS5 | 261 JS5 | 326 JS5 | 391 JS5 | 456 JS5 | 520 JS5 |
11 | 85 JR1 | 161 JS5 | 240 JS5 | 320 JS5 | 399 JS5 | 478 JS5 | 558 JS5 | 637 JS5 |
12 | 106 JR2 | 194 JS5 | 289 JS5 | 385 JS5 | 480 JS5 | 576 JS5 | 671 JS5 | 767 JS5 |
13 | 127 JS1 | 229 LN | 343 JS5 | 456 JS5 | 569 JS5 | 683 JS5 | 796 JS5 | 909 JS5 |
14 | 151 JS1 | 268 LN | 401 JS5 | 534 JS5 | 667 JS5 | 800 JS5 | 933 JS5 | 1066 JS5 |
15 | 177 JS1 | 311 JS5 | 464 JS5 | 618 JS5 | 772 JS5 | 926 JS5 | 1080 JS5 | 1234 JS5 |
J\I | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|
1 | 9 T | 10 T | 11 T | 12 T | 13 T | 14 T | 15 T |
2 | 27 T | 31 F | 34 F | 36 T | 39 T | 43 F | 46 F |
3 | 54 T | 60 T | 66 T | 72 T | 78 T | 84 T | 90 T |
4 | 91 F | 100 T | 111 F | 120 T | 131 F | 140 T | 151 F |
5 | 138 JS5 | 153 JS5 | 168 JS5 | 183 JS5 | 199 JS5 | 214 JS5 | 229 JS5 |
6 | 203 JS5 | 225 JS5 | 248 JS5 | 270 JS5 | 292 JS5 | 315 JS5 | 337 JS5 |
7 | 278 JS5 | 309 JS5 | 339 JS5 | 370 JS5 | 401 JS5 | 431 JS5 | 462 JS5 |
8 | 367 JS5 | 408 JS5 | 448 JS5 | 489 JS5 | 529 JS5 | 570 JS5 | 610 JS5 |
9 | 469 JS5 | 521 JS5 | 572 JS5 | 624 JS5 | 676 JS5 | 728 JS5 | 780 JS5 |
10 | 585 JS5 | 650 JS5 | 715 JS5 | 780 JS5 | 844 JS5 | 909 JS5 | 974 JS5 |
11 | 716 JS5 | 796 JS5 | 875 JS5 | 954 JS5 | 1034 JS5 | 1113 JS5 | 1193 JS5 |
12 | 862 JS5 | 958 JS5 | 1054 JS5 | 1149 JS5 | 1245 JS5 | 1340 JS5 | 1436 JS5 |
13 | 1023 JS5 | 1136 JS5 | 1249 JS5 | 1363 JS5 | 1476 JS5 | 1589 JS5 | 1703 JS5 |
14 | 1198 JS5 | 1331 JS5 | 1464 JS5 | 1597 JS5 | 1730 JS5 | 1863 JS5 | 1996 JS5 |
15 | 1338 JS5 | 1542 JS5 | 1696 JS5 | 1850 JS5 | 2003 JS5 | 2157 JS5 | 2311 JS5 |
References for the tables above.
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