ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=7,t,m,l=1) <= b :

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

Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 7 
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+
----------------------------------------------------------------------
  7:        1 *        1 *        1 *        1 *        1 *        1 *
  8:        3 *        1 *        1 *        1 *        1 *        1 *
  9:        3 *        2 *        1 *        1 *        1 *        1 *
 10:        3 *        2 *        2 *        1 *        1 *        1 *
 11:        4 *        2 *        2 *        2 *        1 *        1 *
 12:        5          2 *        2 *        2 *        2 *        1 *
 13:        6          2 *        2 *        2 *        2 *        2 *
 14:        6 *        2 *        2 *        2 *        2 *        2 *
 15:        7 *        4          2 *        2 *        2 *        2 *
 16:        8          4          3          2 *        2 *        2 *
 17:        9          4          3          3          2 *        2 *
 18:       10          5          3          3          3          2 *
 19:       11          6          3 *        3          3          3  
 20:       12 *        6          3 *        3          3          3  
 21:       13          7          3 *        3          3          3  
 22:       13 *        8          5          3          3          3  
 23:       16          9          5          4          3          3  
 24:       17          9          5          4          4          3  
 25:       18         10          6          4          4          4  
 26:       20         11          7          4          4          4  
 27:       20 *       12          7          4          4          4  
 28:       22         12          8          4          4          4  
 29:       24         13          9          6          4          4  
 30:       25         14          9          6          5          4  
 31:       26         15         10          6          5          5  
 32:       31         16         11          7          5          5  
 33:       33         17         12          8          5          5  
 34:       38         18         12          8          5          5  
 35:       40         19         13          9          5          5  
 36:       45         19         14         10          7          5  
 37:       47         20         15         10          7          6  
 38:       53         21         15         11          7          6  
 39:       55         22         16         12          8          6  
 40:       56         23         17         12          9          6  
 41:       56         24         18         13          9          6  
 42:       56         25         18         14         10          6  
 43:       56         26         19         15         11          8  
 44:       56         26         20         15         11          8  
 45:       56         29         21         16         12          8  
 46:       56         30         22         17         13          9  
 47:       56         31         23         18         13         10  
 48:       56         33         24         18         14         10  
 49:       56.*       33         25         19         15         11  
 50:       65 *       35         25         20         15         12  
 51:       66 *       37         26         21         16         12  
 52:       75         38         27         21         17         13  
 53:       77         39         28         22         18         14  
 54:       86         40         29         23         18         14  

\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  7:        1 *        1 *        1 *        1 *        1 *
  8:        4 *        1 *        1 *        1 *        1 *
  9:        4 *        3          1 *        1 *        1 *
 10:        6 *        3          2 *        1 *        1 *
 11:        8 *        3          2 *        2 *        1 *
 12:       11          4          2 *        2 *        2 *
 13:       13          6          2 *        2 *        2 *
 14:       15          8          2 *        2 *        2 *
 15:       15 *       11          5          2 *        2 *
 16:       25         14          5          4          2 *
 17:       28         17          7          4          3  
 18:       34         20          8          4          3  
 19:       44         26         10          5          3  
 20:       50         29         12          7          3 *
 21:       53         36         14          8          3 *
 22:       66         41         16         10          6  
 23:       74         49         19         12          6  
 24:       90         55         19         14          8  
 25:      102         63         21         16          9  
 26:      116         69         23         18         11  
 27:      130         80         26         19         12  
 28:      152         88         28         21         14  
 29:      155        100         30         23         16  
 30:      155        111         30         26         18  
 31:      155        124         40         29         20  
 32:      186        137         43         32         22  
 33:      205        151         49         35         23  
 34:      239        165         56         41         25  
 35:      259        181         62         44         27  
 36:      301        196         68         51         29  
 37:      322        214         78         56         31  
 38:      368        230         81         63         34  
 39:      390        249         87         69         34  
 40:      442        266         97         75         36  
 41:      468        288        103         82         38  
 42:      523        306        106         89         41  
 43:      550        330        119         94         43  
 44:      616        348        127        102         45  
 45:      646        378        140        108         45  
 46:      715        397        148        116         55  
 47:      745        429        164        122         58  
 48:      826        448        176        133         64  
 49:      859        486        189        141         71  
 50:      938        506        199        153         77  
 51:      989        546        205        162         83  
 52:     1066        566        208        174         90  
 53:     1129        613        221        185         96  
 54:     1206        634        229        198        102  

\t/m        4/4        4/5        4/6        4/7
v\        3+/3+      3+/4+      3+/5+      3+/6+
------------------------------------------------
  7:        1 *        1 *        1 *        1 *
  8:        5 *        1 *        1 *        1 *
  9:        6 *        3          1 *        1 *
 10:       10 *        3          3          1 *
 11:       17          5          3          2 *
 12:       24          8          4          2 *
 13:       30         11          5          2 *
 14:       44         17          7          2 *
 15:       57         24         12          6  
 16:       86         37         17          7  
 17:      114         45         25         11  
 18:      152         60         29         12  
 19:      182         73         39         16  
 20:      225         91         49         20  
 21:      245        115         59         27  
 22:      253        141         75         34  
 23:      253.*      171         92         40  
 24:      357 *      209        110         47  
 25:      443        249        132         54  
 26:      573        281        152         60  
 27:      673        309        186         74  
 28:      833        354        213         87  
 29:      978        398        255        101  
 30:     1194        434        299        114  
 31:     1401        526        342        143  
 32:     1677        579        400        171  
 33:     1941        655        435        200  
 34:     2278        712        489        228  
 35:     2613        792        519        266  
 36:     3018        843        569        283  
 37:     3413       1035        605        297  
 38:     3896       1149        706        310  
 39:     4368       1308        757        339  
 40:     4931       1496        873        367  
 41:     5489       1721        935        405  
 42:     6142       1941       1073        435  
 43:     6782       2171       1181        478  
 44:     7544       2421       1298        498  
 45:     8289       2710       1342        506  
 46:     9153       3023       1452        506  
 47:                3369       1600        610  
 48:                3741       1774        696  
 49:                4107       1928        800  
 50:                4479       2103        886  
 51:                4923       2322       1016  
 52:                5359       2504       1116  
 53:                5856       2764       1246  
 54:                6404       2998       1346  

\t/m        5/5        5/6        5/7
v\        4+/4+      4+/5+      4+/6+
-------------------------------------
  7:        1 *        1 *        1 *
  8:        6 *        1 *        1 *
  9:        9 *        4          1 *
 10:       20 *        5          3  
 11:       34         10          3 *
 12:       59         17          6  
 13:       78         28         10  
 14:      143         47         20  
 15:      203         77         32  
 16:      321        112         51  
 17:      408        154         70  
 18:      618        220         95  
 19:      772        287        135  
 20:     1115        416        178  
 21:     1424        543        243  
 22:     1938        721        347  
 23:     2405        884        457  
 24:     3094       1144        571  
 25:     3772       1461        716  
 26:     4373       1880        895  
 27:     4680       2436       1163  
 28:     4680.*     2940       1422  
 29:     6169 *     3712       1754  
 30:     7912       4428       2188  
 31:                5453       2632  
 32:                6558       3235  
 33:                7915       3732  
 34:                9170       4525  
 35:                           5248  
 36:                           6249  
 37:                           7172  
 38:                           8432  
 39:                           9696  
 40:                                 
 41:                                 
 42:                                 
 43:         .                       
 44:                                 
 45:                                 
 46:                                 
 47:                                 
 48:                                 
 49:                                 
 50:                                 
 51:                                 
 52:         .                       
 53:                                 
 54:                                 

\t/m        6/6        6/7
v\        5+/5+      5+/6+
--------------------------
  7:        1 *        1 *
  8:        7 *        1 *
  9:       16 *        4  
 10:       45 *        8  
 11:       84         19  
 12:      177         35  
 13:      264         62  
 14:      509        100  
 15:      853        205  
 16:     1450        378  
 17:     2165        587  
 18:     3392        888  
 19:     4732       1335  
 20:     6938       2023  
 21:     9648       3049  
 22:                4436  
 23:         .      6275  
 24:                8669  
 25:         .            
 26:                      
 27:                      
 28:                      
 29:         .            
 30:                      
 31:                      
 32:                      
 33:                      
 34:                      
 35:         .            
 36:                      
 37:         .            
 38:                      
 39:                      
 40:                      
 41:                      
 42:                      
 43:         .            
 44:                      
 45:                      
 46:                      
 47:         .            
 48:                      
 49:         .            
 50:                      
 51:                      
 52:                      
 53:         .            
 54:                      

\t/m        7/7
v\        6+/6+
---------------
  7:        1 *
  8:        8 *
  9:       36 *
 10:      120 *
 11:      330 *
 12:      792 *
 13:     1716 *
 14:     3432 *
 15:     6435 *
 16:    11440 *
 17:    19448 *
 18:    31824 *
 19:    50388 *
 20:    77520 *
 21:   116280 *
 22:   170544 *
 23:   245157 *
 24:   346104 *
 25:   480700 *
 26:   657800 *
 27:   888030 *
 28:  1184040 *
 29:  1560780 *
 30:  2035800 *
 31:  2629575 *
 32:  3365856 *
 33:  4272048 *
 34:  5379616 *
 35:  6724520 *
 36:  8347680 *
 37: 10295472 *
 38: 12620256 *
 39: 15380937 *
 40: 18643560 *
 41: 22481940 *
 42: 26978328 *
 43: 32224114 *
 44: 38320568 *
 45: 45379620 *
 46: 53524680 *
 47: 62891499 *
 48: 73629072 *
 49: 85900584 *
 50: 99884400 *
 51:115775100 *
 52:133784560 *
 53:154143080 *
 54:177100560 *

