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

Date  : Sun Sep 29 19:26:40 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:       31         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:       48         24         16         12          9          6  
 36:       50         24         17         12          9          6  
 37:       54         27         17         13         10          8  
 38:       57         28         18         14         11          8  
 39:       60         29         20         15         11          8  
 40:       64         31         20         16         12          9  
 41:       67         33         21         16         13         10  
 42:       70         34         21         17         13         10  
 43:       73         35         24         18         14         11  
 44:       79         36         24         19         15         12  
 45:       82         38         26         20         15         12  
 46:       85         40         26         20         16         13  
 47:       90         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         79         36         22         15  
 26:      130.*       88         40         26         16  
 27:      167 *       91         46         27         19  
 28:      189        108         50         31         22  
 29:      226        122         56         36         23  
 30:      237        132         62         41         26  
 31:      285        154         69         46         29  
 32:      312        167         73         51         32  
 33:      363        188         79         57         33  
 34:      400        203         86         63         37  
 35:      454        212         92         69         41  
 36:      494        240         96         74         45  
 37:      546        263        108         80         51  
 38:      591        294        115         87         55  
 39:      642        320        121         96         61  
 40:      686        353        125        102         65  
 41:      743        384        143        109         71  
 42:      800        419        151        116         75  
 43:      855        454        154        125         81  
 44:      915        493        154        131         87  
 45:      977        530        181        139         93  
 46:     1045        571        193        147         98  
 47:     1111        615        207        156        104  
 48:     1182        658        207        165        110  
 49:     1259        704        234        168        117  
 50:     1338        754        246        185        121  
 51:     1455        802        260        199        127  
 52:     1551        854        260        209        134  
 53:     1672        911        297        221        140  
 54:     1772        965        319        238        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         34         14          8  
 15:      120         44         21         12  
 16:      160         57         30         14  
 17:      211         74         38         19  
 18:      252         81         42         24  
 19:      346        131         54         32  
 20:      434        180         72         40  
 21:      577        204        104         52  
 22:      711        266        121         61  
 23:      784        303        139         73  
 24:      784        381        164         82  
 25:     1026        444        206        107  
 26:     1170        563        268        121  
 27:     1170.*      640        303        146  
 28:     1489 *      772        356        160  
 29:     1803        858        442        200  
 30:     2238       1029        503        240  
 31:     2679       1158        603        280  
 32:     3237       1368        668        320  
 33:     3814       1446        793        371  
 34:     4319       1647        866        412  
 35:     4866       1883       1001        463  
 36:     5456       2034       1080        504  
 37:     6100       2238       1262        598  
 38:     6800       2563       1430        686  
 39:     7551       2793       1658        780  
 40:     8376       3003       1796        868  
 41:     9241       3337       2020        995  
 42:         .      3561       2116       1036  
 43:                4160       2426       1130  
 44:                4455       2613       1218  
 45:                5091       2838       1361  
 46:                5587       3205       1495  
 47:                6226       3433       1568  
 48:                6854       3593       1568  
 49:                7717       4040       1810  
 50:                8472       4294       1954  
 51:         .      9377       4609       1954  
 52:                           5018       2196  
 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.*       41         14  
 13:      245 *       62         28  
 14:      378        112         45  
 15:      610        176         75  
 16:      808        272        129  
 17:     1227        396        191  
 18:     1729        550        245  
 19:     2425        786        352  
 20:     3223       1059        489  
 21:     4348       1428        688  
 22:     5642       1863        933  
 23:     7084       2432       1262  
 24:     7084.*     3108       1660  
 25:     9321 *     3922       2171  
 26:                5192       2778  
 27:                6659       3529  
 28:         .      8457       4402  
 29:                           5457  
 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 *      515  
 15:     5005 *      963  
 16:     8008 *     1687  
 17:    12376 *     2648  
 18:    18564 *     4140  
 19:    27132 *     6458  
 20:    38760 *     9882  
 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 *           

