ENUMERATED STEINER SYSTEMS, t-DESIGNS, COVERINGS C(v,k=4,t,m,l=1) <= b :

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

Global limits:      Current limits:
--------------      ---------------
k <= 35 ( 7)        k  = 4 
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+
----------------------------------------------------------------------
  4:        1 *        1 *        1 *        1 *        1 *        1 *
  5:        3 *        1 *        1 *        1 *        1 *        1 *
  6:        3 *        2 *        1 *        1 *        1 *        1 *
  7:        5 *        2 *        2 *        1 *        1 *        1 *
  8:        6 *        2 *        2 *        2 *        1 *        1 *
  9:        8 *        4          2 *        2 *        2 *        1 *
 10:        9 *        4          3          2 *        2 *        2 *
 11:       11 *        6          3 *        3          2 *        2 *
 12:       12 *        6          3 *        3          3          2 *
 13:       13.*        8          5          3          3          3  
 14:       18 *        9          5          4          3          3  
 15:       19 *       11          7          4          4          3  
 16:       20.*       12          7          4          4          4  
 17:       26 *       14          9          6          4          4  
 18:       27 *       15          9          6          5          4  
 19:       31 *       16         11          8          5          5  
 20:       35 *       18         12          8          5          5  
 21:       37 *       19         14         10          7          5  
 22:       39 *       21         15         10          7          6  
 23:       46 *       22         17         12          9          6  
 24:       48 *       24         18         12          9          6  
 25:       50.*       25         19         14         11          8  
 26:       59 *       26         21         15         11          8  
 27:       61 *       31         22         17         13         10  
 28:       63.*       32         24         18         13         10  
 29:       73 *       33         25         20         15         12  
 30:       75 *       38         27         21         15         12  
 31:       78 *       39         28         22         17         14  
 32:       88 *       40         29         24         18         14  
 33:       91 *       46         31         25         20         16  
 34:       94 *       47         32         27         21         16  
 35:      105 *       51         34         28         23         18  
 36:      108 *       54         35         30         24         18  
 37:      111.*       57         37         31         25         20  
 38:      124 *       59         38         32         27         21  
 39:      127 *       64         39         34         28         23  
 40:      130.*       66         44         35         30         24  
 41:      144 *       70         45         37         31         26  
 42:      147 *       74         46         38         33         27  
 43:      151 *       76         51         40         34         28  
 44:      165 *       78         52         41         35         30  
 45:      169 *       85         53         42         37         31  
 46:      173 *       87         58         44         38         33  
 47:      188 *       89         59         45         40         34  
 48:      192 *       96         60         47         41         36  
 49:      196.*       98         66         48         43         37  
 50:      213 *      100         67         50         44         38  
 51:      217 *      109         71         51         45         40  
 52:      221.*      111         74         52         47         41  
 53:      239 *      113         77         57         48         43  
 54:      243 *      122         79         58         50         44  

\t/m        3/3        3/4        3/5        3/6        3/7
v\        2+/2+      2+/3+      2+/4+      2+/5+      2+/6+
-----------------------------------------------------------
  4:        1 *        1 *        1 *        1 *        1 *
  5:        4 *        1 *        1 *        1 *        1 *
  6:        6 *        3          1 *        1 *        1 *
  7:       12 *        4          2 *        1 *        1 *
  8:       14.*        6          2 *        2 *        1 *
  9:       25 *        9          5          2 *        2 *
 10:       30.*       14          7          4          2 *
 11:       47 *       19         10          5          3  
 12:       57 *       26         12          7          3 *
 13:       78 *       34         13         10          6  
 14:       91.*       43         20         12          8  
 15:      124 *       54         26         15         10  
 16:      140.*       66         28         20         12  
 17:      183 *       83         39         23         14  
 18:      207 *       99         44         28         17  
 19:      261        118         55         33         19  
 20:      285.*      133         60         40         25  
 21:      352 *      147         77         48         27  
 22:      385.*      179         87         56         34  
 23:      466 *      196        104         64         40  
 24:      510 *      237        114         73         42  
 25:      600 *      255        135         84         53  
 26:      650.*      298        148         96         58  
 27:      763 *      324        169        111         69  
 28:      819.*      380        182        123         74  
 29:      950 *      411        215        140         85  
 30:     1020 *      472        231        156         90  
 31:     1170        512        264        174        107  
 32:     1240.*      580        280        190        117  
 33:     1411 *      627        323        204        134  
 34:     1496.*      701        347        224        144  
 35:     1689 *      742        390        238        161  
 36:     1791 *      826        414        270        171  
 37:     1998 *      871        468        287        192  
 38:     2109.*      962        492        319        205  
 39:     2350 *     1014        546        336        226  
 40:     2470.*     1130        570        377        239  
 41:     2737 *     1252        637        395        260  
 42:     2877 *     1380        670        438        273  
 43:     3171       1443        737        462        306  
 44:     3311.*     1508        770        505        322  
 45:     3634 *     1575        851        531        355  
 46:     3795.*     1729        895        583        371  
 47:     4148 *     1815        976        609        404  
 48:     4332 *     1971       1020        665        420  
 49:     4716       2154       1110        696        463  
 50:     4900.*     2254       1160        757        487  
 51:     5317 *     2360       1250        796        530  
 52:     5525.*     2539       1300        857        554  
 53:     5976 *     2725       1413        897        597  
 54:     6210 *     2829       1469        965        621  

\t/m        4/4        4/5        4/6        4/7
v\        3+/3+      3+/4+      3+/5+      3+/6+
------------------------------------------------
  4:        1 *        1 *        1 *        1 *
  5:        5 *        1 *        1 *        1 *
  6:       15 *        3 *        1 *        1 *
  7:       35 *        7 *        3 *        1 *
  8:       70 *       14 *        6          2 *
  9:      126 *       30         12          5  
 10:      210 *       50         20         10  
 11:      330 *       84         34         17  
 12:      495 *      126         56         28  
 13:      715 *      193         90         47  
 14:     1001 *      289        142         70  
 15:     1365 *      414        212        105  
 16:     1820 *      563        303        140  
 17:     2380 *      761        415        196  
 18:     3060 *     1015        554        252  
 19:     3876 *     1333        722        336  
 20:     4845 *     1723        926        420  
 21:     5985 *     2194       1166        540  
 22:     7315 *     2748       1451        660  
 23:     8855 *     3394       1781        825  
 24:    10626 *     4140       2166        990  
 25:    12650 *     5000       2606       1210  
 26:    14950 *     5977       3112       1430  
 27:    17550 *     7078       3684       1716  
 28:    20475 *     8319       4334       2002  
 29:    23751 *     9713       5062       2366  
 30:    27405 *                5881       2730  
 31:    31465 *                6791       3185  
 32:    35960 *                7806       3640  
 33:    40920 *                8926       4200  
 34:    46376 *                           4760  
 35:    52360 *                           5440  
 36:    58905 *                           6120  
 37:    66045 *                           6936  
 38:    73815 *                           7752  
 39:    82251 *                           8721  
 40:    91390 *                           9690  
 41:   101270 *                                 
 42:   111930 *                                 
 43:   123410 *                                 
 44:   135751 *                                 
 45:   148995 *                                 
 46:   163185 *                                 
 47:   178365 *                                 
 48:   194580 *                                 
 49:   211876 *                                 
 50:   230300 *                                 
 51:   249900 *                                 
 52:   270725 *                                 
 53:   292825 *                                 
 54:   316251 *                                 

