ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=5,t,m,l=1) <= b :

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

Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 5 
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+
----------------------------------------------------------------------
  5:        1 *        1 *        1 *        1 *        1 *        1 *
  6:        3 *        1 *        1 *        1 *        1 *        1 *
  7:        3 *        2 *        1 *        1 *        1 *        1 *
  8:        4 *        2 *        2 *        1 *        1 *        1 *
  9:        5 *        2 *        2 *        2 *        1 *        1 *
 10:        6 *        2 *        2 *        2 *        2 *        1 *
 11:        7 *        4          2 *        2 *        2 *        2 *
 12:        9 *        4          3          2 *        2 *        2 *
 13:       10 *        5          3          3          2 *        2 *
 14:       12 *        6          3 *        3          3          2 *
 15:       13 *        7          3 *        3          3          3  
 16:       15 *        8          5          3          3          3  
 17:       16 *        9          5          4          3          3  
 18:       18 *       10          6          4          4          3  
 19:       19 *       11          7          4          4          4  
 20:       21 *       12          8          4          4          4  
 21:       21.*       13          9          6          4          4  
 22:       27 *       14         10          6          5          4  
 23:       28 *       16         11          7          5          5  
 24:       30 *       17         12          8          5          5  
 25:       30.*       18         13          9          5          5  
 26:       37 *       20         14         10          7          5  
 27:       38 *       21         15         11          7          6  
 28:       42         23         16         12          8          6  
 29:       44         25         17         13          9          6  
 30:       48 *       26         18         14         10          6  
 31:       50 *       27         19         15         11          8  
 32:       53         28         20         16         12          8  
 33:       54 *       30         21         17         13          9  
 34:       62 *       31         23         18         14         10  
 35:       63 *       33         24         19         15         11  
 36:       67         34         25         20         16         12  
 37:       68 *       36         27         21         17         13  
 38:       76 *       37         28         22         18         14  
 39:       78 *       39         30         23         19         15  
 40:       82         40         31         24         20         16  
 41:       82.*       42         33         25         21         17  
 42:       93 *       42         34         26         22         18  
 43:       96         48         35         27         23         19  
 44:       99         49         37         28         24         20  
 45:       99.*       51         38         30         25         21  
 46:      111 *       51         39         31         26         22  
 47:      114         57         41         32         27         23  
 48:      122         58         42         34         28         24  
 49:      130         60         44         35         29         25  
 50:      130 *       60         46         36         30         26  
 51:      140         67         47         38         31         27  
 52:      140         68         48         39         32         28  
 53:      140 *       72         49         41         33         29  
 54:      152 *       74         51         42         34         30  

\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  5:        1 *        1 *        1 *        1 *        1 *
  6:        4 *        1 *        1 *        1 *        1 *
  7:        5 *        3          1 *        1 *        1 *
  8:        8 *        3          2 *        1 *        1 *
  9:       12 *        5          2 *        2 *        1 *
 10:       17 *        7          2 *        2 *        2 *
 11:       20 *        9          5          2 *        2 *
 12:       29         12          6          4          2 *
 13:       34         16          8          4          3  
 14:       43         20         10          6          3  
 15:       57         25         13          8          3 *
 16:       67         33         14         10          6  
 17:       68.*       40         18         12          7  
 18:       94 *       49         23         14          9  
 19:      113         59         28         17         11  
 20:      138         72         32         20         13  
 21:      151         84         37         24         15  
 22:      184         95         40         28         18  
 23:      190        103         49         32         19  
 24:      234        116         54         36         22  
 25:      259        137         63         40         26  
 26:      260.*      156         68         45         30  
 27:      319 *      176         77         53         34  
 28:      372        197         86         59         38  
 29:      433        215         97         67         43  
 30:      483        231        102         74         48  
 31:      540        258        111         83         52  
 32:      601        280        125         92         57  
 33:      672        314        135        101         60  
 34:      740        360        136        108         69  
 35:      802        402        162        117         74  
 36:      878        435        181        127         83  
 37:      955        452        206        140         88  
 38:     1035        479        219        152         97  
 39:     1121        516        245        163        102  
 40:     1211        557        258        171        111  
 41:     1294        596        284        184        120  
 42:     1402        656        302        205        129  
 43:     1507        701        328        224        136  
 44:     1609        771        341        244        145  
 45:     1716        815        373        265        154  
 46:     1837        859        380        283        165  
 47:     1957        900        411        299        170  
 48:     2091        960        444        325        179  
 49:     2222       1054        450        344        193  
 50:     2358       1144        494        366        203  
 51:     2569       1244        519        382        204  
 52:     2775       1342        520        405        230  
 53:     2974       1453        579        421        249  
 54:     3213       1559        632        448        274  

\t/m        4/4        4/5        4/6        4/7
v\        3+/3+      3+/4+      3+/5+      3+/6+
------------------------------------------------
  5:        1 *        1 *        1 *        1 *
  6:        5 *        1 *        1 *        1 *
  7:        9 *        3          1 *        1 *
  8:       20 *        5          3          1 *
  9:       30 *        9          4          2 *
 10:       51         14          7          2 *
 11:       66.*       22         10          5  
 12:      113 *       35         17          8  
 13:      157         50         27         14  
 14:      232         74         39         18  
 15:      300         99         54         28  
 16:      419        136         68         39  
 17:      492        193         68         50  
 18:      671        262        107         60  
 19:      850        341        144         81  
 20:     1096        415        199         96  
 21:     1251        492        252        117  
 22:     1573        624        329        132  
 23:     1771.*      789        407        179  
 24:     2237 *      971        511        223  
 25:     2706       1099        616        270  
 26:     3306       1269        751        314  
 27:     3906       1482        886        389  
 28:     4669       1768       1054        457  
 29:     5427       2083       1224        532  
 30:     6232       2436       1439        600  
 31:     6780       2711       1650        719  
 32:     7785       3010       1913        792  
 33:     8930       3333       2152        911  
 34:                3883       2475        984  
 35:         .      4469       2799       1163  
 36:                5091       3175       1342  
 37:                5555       3545       1521  
 38:                6043       4010       1700  
 39:                6555       4472       1922  
 40:                7520       5018       2101  
 41:         .      8565       5514       2347  
 42:                9684       6151       2502  
 43:                           6783       2824  
 44:                           7519       3022  
 45:         .                 8232       3344  
 46:                           9076       3542  
 47:    35673.*                9937       4008  
 48:    39821 *                           4474  
 49:                                      4943  
 50:                                      5412  
 51:         .                            6012  
 52:                                      6612  
 53:         .                            7212  
 54:                                      7812  

\t/m        5/5        5/6        5/7
v\        4+/4+      4+/5+      4+/6+
-------------------------------------
  5:        1 *        1 *        1 *
  6:        6 *        1 *        1 *
  7:       21 *        4 *        1 *
  8:       56 *       11          3 *
  9:      126 *       25          8  
 10:      252 *       51         17  
 11:      462 *      100         32  
 12:      792 *      177         59  
 13:     1287 *      303        110  
 14:     2002 *      496        200  
 15:     3003 *      784        342  
 16:     4368 *     1196        554  
 17:     6188 *     1759        857  
 18:     8568 *     2520       1272  
 19:    11628 *     3535       1826  
 20:    15504 *     4868       2548  
 21:    20349 *     6591       3474  
 22:    26334 *     8785       4640  
 23:    33649 *                6091  
 24:    42504 *                7872  
 25:    53130 *                      
 26:    65780 *                      
 27:    80730 *                      
 28:    98280 *                      
 29:   118755 *                      
 30:   142506 *                      
 31:   169911 *                      
 32:   201376 *                      
 33:   237336 *                      
 34:   278256 *                      
 35:   324632 *                      
 36:   376992 *                      
 37:   435897 *                      
 38:   501942 *                      
 39:   575757 *                      
 40:   658008 *                      
 41:   749398 *                      
 42:   850668 *                      
 43:   962598 *                      
 44:  1086008 *                      
 45:  1221759 *                      
 46:  1370754 *                      
 47:  1533939 *                      
 48:  1712304 *                      
 49:  1906884 *                      
 50:  2118760 *                      
 51:  2349060 *                      
 52:  2598960 *                      
 53:  2869685 *                      
 54:  3162510 *                      

