ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=6,t,m,l=1) <= b :

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

Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 6 
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+
----------------------------------------------------------------------
  6:        1 *        1 *        1 *        1 *        1 *        1 *
  7:        3 *        1 *        1 *        1 *        1 *        1 *
  8:        3 *        2 *        1 *        1 *        1 *        1 *
  9:        3 *        2 *        2 *        1 *        1 *        1 *
 10:        4 *        2 *        2 *        2 *        1 *        1 *
 11:        6 *        2 *        2 *        2 *        2 *        1 *
 12:        6 *        2 *        2 *        2 *        2 *        2 *
 13:        7 *        4          2 *        2 *        2 *        2 *
 14:        7 *        4          3          2 *        2 *        2 *
 15:       10          4          3          3          2 *        2 *
 16:       10          5          3 *        3          3          2 *
 17:       12 *        6          3 *        3          3          3  
 18:       12 *        6          3 *        3          3          3  
 19:       15          7          5          3          3          3  
 20:       16          8          5          4          3          3  
 21:       17          9          5          4          4          3  
 22:       19 *       10          6          4          4          4  
 23:       21 *       10          7          4          4          4  
 24:       22 *       11          7          4          4          4  
 25:       23 *       13          8          6          4          4  
 26:       24         13          9          6          5          4  
 27:       27 *       14          9          6          5          5  
 28:       28 *       14         10          7          5          5  
 29:       30         17         11          8          5          5  
 30:       31         17         12          8          5          5  
 31:       31.*       19         13          9          7          5  
 32:       38 *       19         13         10          7          6  
 33:       39 *       22         14         10          7          6  
 34:       42 *       22         15         11          8          6  
 35:       47         24         16         12          9          6  
 36:       50         24         17         12          9          6  
 37:       53         27         17         13         10          8  
 38:       57         28         18         14         11          8  
 39:       59         29         20         15         11          8  
 40:       59         31         20         16         12          9  
 41:       61         33         21         16         13         10  
 42:       63 *       34         21         17         13         10  
 43:       67         35         24         18         14         11  
 44:       71         36         24         19         15         12  
 45:       77         38         26         20         15         12  
 46:       81         40         26         20         16         13  
 47:       86         41         29         21         17         14  
 48:       93         43         29         22         18         14  
 49:       97         43         31         23         19         15  
 50:      100         46         31         24         19         16  
 51:      110         47         34         24         20         16  
 52:      113         48         34         25         21         17  
 53:      117         50         36         27         22         18  
 54:      117         52         36         27         23         18  

\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  6:        1 *        1 *        1 *        1 *        1 *
  7:        4 *        1 *        1 *        1 *        1 *
  8:        4 *        3          1 *        1 *        1 *
  9:        7          3          2 *        1 *        1 *
 10:       10 *        4          2 *        2 *        1 *
 11:       11 *        5          2 *        2 *        2 *
 12:       15          6          2 *        2 *        2 *
 13:       21          9          5          2 *        2 *
 14:       25         11          5          4          2 *
 15:       31         15          8          4          3  
 16:       38         16          8          5          3  
 17:       44         21         11          6          3 *
 18:       48         26         12          7          3 *
 19:       66         32         15          9          6  
 20:       74         39         18         10          6  
 21:       77         48         21         13          9  
 22:       77.*       54         22         15          9  
 23:      104 *       64         26         17         11  
 24:      116         70         30         20         12  
 25:      130         77         36         22         15  
 26:      130.*       88         40         26         16  
 27:      167 *       91         46         27         19  
 28:      189        106         50         31         22  
 29:      226        121         56         36         23  
 30:      237        132         62         41         26  
 31:      285        154         69         46         29  
 32:      312        165         73         51         32  
 33:      363        185         79         57         33  
 34:      400        199         86         63         37  
 35:      454        212         92         69         41  
 36:      494        239         96         74         45  
 37:      546        263        108         80         51  
 38:      591        288        115         87         55  
 39:      642        308        121         96         61  
 40:      686        326        125        102         65  
 41:      743        353        143        109         71  
 42:      800        372        151        116         75  
 43:      855        406        154        125         81  
 44:      915        424        154        131         87  
 45:      977        445        181        139         93  
 46:     1045        451        193        147         98  
 47:     1111        475        207        154        104  
 48:     1182        480        207        165        110  
 49:     1259        537        234        168        117  
 50:     1338        574        246        183        121  
 51:     1455        634        260        198        127  
 52:     1551        674        260        209        134  
 53:     1672        742        297        221        140  
 54:     1772        785        319        236        144  

\t/m        4/4        4/5        4/6        4/7
v\        3+/3+      3+/4+      3+/5+      3+/6+
------------------------------------------------
  6:        1 *        1 *        1 *        1 *
  7:        5 *        1 *        1 *        1 *
  8:        7 *        3          1 *        1 *
  9:       12 *        3 *        3          1 *
 10:       20 *        7          3          2 *
 11:       32         10          5          2 *
 12:       41         14          6          2 *
 13:       66         21         10          5  
 14:       80         32         14          8  
 15:      118         43         21         12  
 16:      160         55         29         14  
 17:      210         74         37         19  
 18:      252         81         42         24  
 19:      343        129         54         32  
 20:      400        149         72         40  
 21:      522        178        104         52  
 22:      580        189        120         61  
 23:      751        260        134         73  
 24:      784        326        164         82  
 25:     1018        419        206        107  
 26:     1170        556        268        121  
 27:     1170.*      630        303        146  
 28:     1489 *      772        356        160  
 29:     1803        858        442        198  
 30:     2236       1025        503        236  
 31:     2678       1155        603        278  
 32:     3217       1357        668        320  
 33:     3784       1446        793        370  
 34:     4318       1644        866        412  
 35:     4863       1843       1001        462  
 36:     5453       2030       1080        504  
 37:     6095       2143       1260        595  
 38:     6796       2556       1396        652  
 39:     7550       2681       1615        743  
 40:     8375       2926       1744        800  
 41:     9241       3337       2002        922  
 42:         .      3526       2116        980  
 43:                4123       2418       1102  
 44:                4438       2579       1160  
 45:                5059       2838       1306  
 46:                5587       3205       1364  
 47:                6219       3399       1535  
 48:                6827       3593       1568  
 49:                7705       3993       1750  
 50:                8406       4294       1921  
 51:         .      9346       4609       1954  
 52:                           5018       2188  
 53:                           5408       2340  
 54:                           5821       2340  

\t/m        5/5        5/6        5/7
v\        4+/4+      4+/5+      4+/6+
-------------------------------------
  6:        1 *        1 *        1 *
  7:        6 *        1 *        1 *
  8:       12 *        4          1 *
  9:       30 *        7          3  
 10:       50         14          4  
 11:      100         22          9  
 12:      132.*       38         14  
 13:      245 *       62         28  
 14:      377        105         45  
 15:      609        173         75  
 16:      808        253        129  
 17:     1227        381        191  
 18:     1548        544        245  
 19:     2210        765        352  
 20:     2900       1026        489  
 21:     3996       1401        688  
 22:     4692       1863        933  
 23:     6203       2428       1262  
 24:     7084.*     3086       1660  
 25:     9321 *     3917       2171  
 26:                4894       2778  
 27:                6142       3529  
 28:         .      7527       4402  
 29:                9295       5456  
 30:                           6668  
 31:                           8107  
 32:                           9737  
 33:                                 
 34:         .                       
 35:                                 
 36:         .                       
 37:                                 
 38:                                 
 39:                                 
 40:                                 
 41:                                 
 42:         .                       
 43:                                 
 44:                                 
 45:                                 
 46:         .                       
 47:                                 
 48:   285384.*                      
 49:   325205 *                      
 50:                                 
 51:                                 
 52:         .                       
 53:                                 
 54:         .                       

\t/m        6/6        6/7
v\        5+/5+      5+/6+
--------------------------
  6:        1 *        1 *
  7:        7 *        1 *
  8:       28 *        4 *
  9:       84 *       12 *
 10:      210 *       30 *
 11:      462 *       66 *
 12:      924 *      132 *
 13:     1716 *      264  
 14:     3003 *      511  
 15:     5005 *      951  
 16:     8008 *     1680  
 17:    12376 *     2648  
 18:    18564 *     4101  
 19:    27132 *     6315  
 20:    38760 *     9544  
 21:    54264 *    14293  
 22:    74613 *           
 23:   100947 *           
 24:   134596 *           
 25:   177100 *           
 26:   230230 *           
 27:   296010 *           
 28:   376740 *           
 29:   475020 *           
 30:   593775 *           
 31:   736281 *           
 32:   906192 *           
 33:  1107568 *           
 34:  1344904 *           
 35:  1623160 *           
 36:  1947792 *           
 37:  2324784 *           
 38:  2760681 *           
 39:  3262623 *           
 40:  3838380 *           
 41:  4496388 *           
 42:  5245786 *           
 43:  6096454 *           
 44:  7059052 *           
 45:  8145060 *           
 46:  9366819 *           
 47: 10737573 *           
 48: 12271512 *           
 49: 13983816 *           
 50: 15890700 *           
 51: 18009460 *           
 52: 20358520 *           
 53: 22957480 *           
 54: 25827165 *           

