ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=3,t,m,l=1) <= b :

Date  : Mon Dec 09 18:27:41 1996
Author: U.Mutlu

Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 3 
l <= 1295           l  = 1 
v <= 255            v <= 54 
b <= 1679615        b <= 9999

Trivial cases are: t=m=k (ie. Complete Design), t=m=1, v=k, (b=1)
"+" means bonus nbr

Key to the signs at the end of the entry b:

 [.] Non-trivial Steiner System with L=1 (exact covering, packing, t-design)
 [*] Schnheim Lower Bound (SLB) or a known higher Exact Lower Bound (ELB) met

\t/m        2/2        2/3        2/4        2/5        2/6        2/7
v\        1+/1+      1+/2+      1+/3+      1+/4+      1+/5+      1+/6+
----------------------------------------------------------------------
  3:        1 *        1 *        1 *        1 *        1 *        1 *
  4:        3 *        1 *        1 *        1 *        1 *        1 *
  5:        4 *        2 *        1 *        1 *        1 *        1 *
  6:        6 *        2 *        2 *        1 *        1 *        1 *
  7:        7.*        4          2 *        2 *        1 *        1 *
  8:       11 *        5          3          2 *        2 *        1 *
  9:       12.*        7          3 *        3          2 *        2 *
 10:       17 *        8          5          3          3          2 *
 11:       19 *       10          6          4          3          3  
 12:       24 *       11          8          4          4          3  
 13:       26.*       13          9          6          4          4  
 14:       33 *       14         11          7          5          4  
 15:       35.*       18         12          9          5          5  
 16:       43 *       19         14         10          7          5  
 17:       46 *       23         15         12          8          6  
 18:       54 *       24         17         13         10          6  
 19:       57.*       29         18         15         11          8  
 20:       67 *       31         20         16         13          9  
 21:       70.*       36         21         18         14         11  
 22:       81 *       38         25         19         16         12  
 23:       85 *       43         26         21         17         14  
 24:       96 *       45         30         22         19         15  
 25:      100.*       50         31         24         20         17  
 26:      113 *       52         35         25         22         18  
 27:      117.*       59         36         27         23         20  
 28:      131 *       61         41         28         25         21  
 29:      136 *       68         43         32         26         23  
 30:      150 *       70         48         33         28         24  
 31:      155.*       78         50         37         29         26  
 32:      171 *       81         55         38         31         27  
 33:      176.*       89         57         42         32         29  
 34:      193 *       92         62         43         34         30  
 35:      199 *      100         64         47         35         32  
 36:      216 *      103         69         48         39         33  
 37:      222.*      111         71         53         40         35  
 38:      241 *      114         76         55         44         36  
 39:      247.*      124         78         60         45         38  
 40:      267 *      127         85         62         49         39  
 41:      274 *      137         87         67         50         41  
 42:      294 *      140         94         69         54         42  
 43:      301.*      151         96         74         55         46  
 44:      323 *      155        103         76         59         47  
 45:      330.*      166        105         81         60         51  
 46:      353 *      170        113         83         65         52  
 47:      361 *      181        116         88         67         56  
 48:      384 *      185        124         90         72         57  
 49:      392.*      196        127         95         74         61  
 50:      417 *      200        135         97         79         62  
 51:      425.*      213        138        102         81         66  
 52:      451 *      217        146        104         86         67  
 53:      460 *      230        149        111         88         71  
 54:      486 *      234        157        113         93         72  

\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  3:        1 *        1 *        1 *        1 *        1 *
  4:        4 *        1 *        1 *        1 *        1 *
  5:       10 *        3 *        1 *        1 *        1 *
  6:       20 *        6          2 *        1 *        1 *
  7:       35 *       12          5          2 *        1 *
  8:       56 *       20          8          4          2 *
  9:       84 *       30         12          7          3 *
 10:      120 *       45         20         10          6  
 11:      165 *       63         29         16          9  
 12:      220 *       84         40         22         12  
 13:      286 *      112         55         30         16  
 14:      364 *      144         70         40         22  
 15:      455 *      181         91         50         30  
 16:      560 *      227        112         65         39  
 17:      680 *      276        139         80         49  
 18:      816 *      335        168         98         60  
 19:      969 *      398        204        119         75  
 20:     1140 *      473        240        140         90  
 21:     1330 *      554        285        168        105  
 22:     1540 *      646        330        196        126  
 23:     1771 *      746        385        228        147  
 24:     2024 *      860        440        264        168  
 25:     2300 *      980        506        301        195  
 26:     2600 *     1114        572        346        223  
 27:     2925 *     1258        650        392        252  
 28:     3276 *     1411        728        441        288  
 29:     3654 *     1585        819        496        324  
 30:     4060 *     1773        910        555        360  
 31:     4495 *     1963       1015        618        405  
 32:     4960 *     2176       1120        684        450  
 33:     5456 *     2410       1240        759        495  
 34:     5984 *     2654       1360        837        550  
 35:     6545 *     2866       1496        918        605  
 36:     7140 *     3148       1632       1009        660  
 37:     7770 *     3454       1785       1101        726  
 38:     8436 *     3778       1938       1201        792  
 39:     9139 *     4120       2109       1306        858  
 40:     9880 *     4481       2280       1420        936  
 41:    10660 *     4861       2470       1540       1014  
 42:    11480 *     5261       2660       1660       1092  
 43:    12341 *     5681       2870       1794       1183  
 44:    13244 *     6112       3080       1930       1274  
 45:    14190 *     6574       3311       2074       1365  
 46:    15180 *     7058       3542       2227       1470  
 47:    16215 *     7564       3795       2380       1575  
 48:    17296 *     8093       4048       2551       1680  
 49:    18424 *     8645       4324       2725       1800  
 50:    19600 *     9221       4600       2913       1920  
 51:    20825 *     9821       4900       3103       2040  
 52:    22100 *                5200       3293       2176  
 53:    23426 *                5525       3503       2312  
 54:    24804 *                5850       3716       2448  

