View source for The Degree Diameter Problem for Circulant Graphs

===Table of the orders of the largest known circulant graphs===

<center> 
{| border="1" cellspacing="2" cellpadding="2" style="text-align: center;"
| '''<math>d</math>\<math>k</math>'''||  '''2''' ||  '''3''' ||  '''4'''|| '''5''' ||  '''6''' || '''7''' ||  '''8''' ||  '''9''' ||  '''10'''  ||  '''11'''  ||  '''12''' 
|-
| '''3''' ||style="background-color: #bbffff;" | '''8'''||style="background-color: #bbffff;" | '''12'''||style="background-color: #bbffff;" | '''16''' ||style="background-color: #bbffff;" | '''20''' ||style="background-color: #bbffff;" | '''24''' ||style="background-color: #bbffff;" | '''28'''||style="background-color: #bbffff;" | '''32''' ||style="background-color: #bbffff;" | '''36''' || style="background-color: #bbffff;" | '''40'''  ||style="background-color: #bbffff;" | '''44'''||style="background-color: #bbffff;" | '''48'''
|-
| '''4''' ||style="background-color: beige;" | '''13'''|| style="background-color: beige;" | '''25''' ||style="background-color: beige;" | '''41''' || style="background-color: beige;" | '''61''' ||style="background-color: beige;" | '''85''' ||style="background-color: beige;" | '''113''' ||style="background-color: beige;" | '''145''' ||style="background-color: beige;" | '''181''' ||style="background-color: beige;" | '''221''' ||style="background-color: beige;" | '''265''' ||style="background-color: beige;" | '''313''' 
|-
| '''5''' ||style="background-color: white;" | '''16''' ||style="background-color: #66cc66;" | '''36''' ||style="background-color: #66cc66;" | '''64''' ||style="background-color: #66cc66;" |  '''100''' ||style="background-color: #66cc66;" | '''144''' ||style="background-color: #66cc66;" |  '''196''' ||style="background-color: #66cc66;" |  '''256''' ||style="background-color: #66cc66;" |  '''324''' ||style="background-color: #66cc66;" |  '''400''' ||style="background-color: #66cc66;" |  '''484''' ||style="background-color: #66cc66;" |  '''576''' 
|-
| '''6''' ||style="background-color: magenta;" | '''21''' ||style="background-color: magenta;" | '''55''' ||style="background-color: magenta;" | '''117''' ||style="background-color: magenta;" | '''203''' ||style="background-color: magenta;" | '''333''' ||style="background-color: magenta;" | '''515''' ||style="background-color: magenta;" | '''737''' ||style="background-color: magenta;" | '''1 027''' ||style="background-color: magenta;" | '''1 393''' ||style="background-color: magenta;" | '''1 815''' ||style="background-color: magenta;" | '''2 329''' 
|-					
| '''7''' ||style="background-color: magenta;" | '''26''' ||style="background-color: magenta;" | '''76'''  ||style="background-color: magenta;" | '''160''' ||style="background-color: magenta;" | '''308''' ||style="background-color: magenta;" | '''536''' ||style="background-color: magenta;" | '''828''' ||style="background-color: magenta;" | '''1 232''' ||style="background-color: magenta;" | '''1 764''' ||style="background-color: magenta;" | '''2 392''' ||style="background-color: magenta;" | 3 180 ||style="background-color: magenta;" | 4 144 
|-						
| '''8''' ||style="background-color: #81BEF7;" | '''35''' ||style="background-color: #CCFF00;" | '''104''' ||style="background-color: #CCFF00;" | '''248''' ||style="background-color: #CCFF00;" | '''528''' ||style="background-color: #66ff66;" | '''984''' ||style="background-color: #66ff66;" | '''1 712''' ||style="background-color: #66ff66;" | 2 768 ||style="background-color: #66ff66;" | 4 280 ||style="background-color: #66ff66;" | 6 320  ||style="background-color: #66ff66;" | 9 048 ||style="background-color: #66ff66;" | 12 552 
|-							
| '''9''' ||style="background-color: #81BEF7;" | '''42''' || style="background-color: #66cc66;" | '''130''' ||style="background-color: #CCFF00;" | '''320''' ||style="background-color: #66ff66;" | '''700''' ||style="background-color: #66ff66;" | '''1 416''' ||style="background-color: #66ff66;" | 2 548 ||style="background-color: #66ff66;" | 4 304 ||style="background-color: #66ff66;" | 6 804 ||style="background-color: #66ff66;" | 10 320  ||style="background-color: #66ff66;" | 15 004 ||style="background-color: #66ff66;" | 21 192 
|-							
| '''10''' ||style="background-color: #81BEF7;" | '''51''' || style="background-color: #66cc66;" | '''177''' ||style="background-color: yellow;" | '''457''' ||style="background-color: #66ff66;" | '''1 099''' ||style="background-color: orange;" | 2 380 ||style="background-color: orange;" | 4 551 ||style="background-color: orange;" | 8 288 ||style="background-color: orange;" | 14 099 ||style="background-color: orange;" | 22 805 ||style="background-color: #66ff66;" | 35 568  ||style="background-color: #66ff66;" | 53 025 
|-	
| '''11''' ||style="background-color: #81BEF7;" | '''56''' ||style="background-color: yellow;" | '''210''' || style="background-color: yellow;" | '''576''' ||style="background-color: orange;" | 1 428 ||style="background-color: orange;" | 3 200 ||style="background-color: orange;" | 6 652 ||style="background-color: orange;" | 12 416 || style="background-color: orange;" | 21 572 ||style="background-color: orange;" |  35 880  ||style="background-color: #66ff66;" | 56 700  ||style="background-color: #66ff66;" | 87 248 
|-
| '''12''' ||style="background-color: #81BEF7;" | '''67''' ||style="background-color: yellow;" | '''275''' ||style="background-color: orange;" | 819 ||style="background-color: #66ff66;" | 2 120 ||style="background-color: #66ff66;" | 5 044 ||style="background-color: #66ff66;" | 10 777 ||style="background-color: #66ff66;" | 21 384  ||style="background-color: #66ff66;" | 39 996 ||style="background-color: #66ff66;" | 69 965 ||style="background-color: #66ff66;" | 117 712  ||style="background-color: #66ff66;" | 190 392
|-
| '''13''' ||style="background-color: #81BEF7;" | '''80''' ||style="background-color: yellow;" | '''312''' ||style="background-color: orange;" | 970 ||style="background-color: #66ff66;" | 2 676 ||style="background-color: #66ff66;" | 6 256 ||style="background-color: #66ff66;" | 14 740 ||style="background-color: #66ff66;" | 30 760  ||style="background-color: #66ff66;" | 57 396 ||style="background-color: #66ff66;" | 106 120 ||style="background-color: #66ff66;" | 182 980  ||style="background-color: #66ff66;" | 295 840 
|-	
| '''14''' ||style="background-color: #81BEF7;" | '''90''' ||style="background-color: yellow;" | '''381''' || style="background-color: orange;" | 1 229 ||style="background-color: #66ff66;" | 3 695 ||style="background-color: #66ff66;" | 9 800 ||style="background-color: #66ff66;" | 23 304 ||style="background-color: #66ff66;" | 49 757 || style="background-color: #66ff66;" | 103 380 ||style="background-color: #66ff66;" |  196 689 ||style="background-color: #66ff66;" | 350 700 || style="background-color: #66ff66;" | 593 989 
|-
| '''15''' ||style="background-color: #81BEF7;" | '''96''' ||style="background-color: yellow;" | '''448''' ||style="background-color: orange;" | 1 420 ||style="background-color: #66ff66;" | 4 292 ||style="background-color: #66ff66;" | 12 232 ||style="background-color: #66ff66;" | 32 092 ||style="background-color: #66ff66;" | 68 944  ||style="background-color: #66ff66;" | 142 516 ||style="background-color: #66ff66;" | 276 928 ||style="background-color: #66ff66;" | 514 580  ||style="background-color: #66ff66;" | 908 480 
|-
| '''16''' ||style="background-color: #81BEF7;" | '''112''' ||style="background-color: orange;" | 518 ||style="background-color: #66ff66;" | 1 788 ||style="background-color: #66ff66;" | 5 847 ||style="background-color: #66ff66;" | 17 733 ||style="background-color: #66ff66;" | 44 328 ||style="background-color: #66ff66;" | 107 748  ||style="background-color: #66ff66;" | 232 245 ||style="background-color: #66ff66;" | 479 255 ||style="background-color: #66ff66;" | 924 420  ||style="background-color: #66ff66;" | 1 702 428 
|-
| '''17''' ||style="background-color: #81BEF7;" | '''130''' || |  || |  ||style="background-color: #66ff66;" | 6 468 ||style="background-color: #66ff66;" | 20 360 ||style="background-color: #66ff66;" | 57 684 ||style="background-color: #66ff66;" | 136 512  ||style="background-color: #66ff66;" | 321 780 ||style="background-color: #66ff66;" | 659 464 ||style="background-color: #66ff66;" | 1 350 820  ||style="background-color: #66ff66;" | 2 479 104 
|}
</center>

The following table is the key to the colors in the table presented above:

<center>
{| border="1" cellspacing="1" cellpadding="1" style="text-align: left;"
|'''Color''' || style="text-align: center;" |'''Details'''
|-
|style="background-color: #ffffff; text-align: center;" | '''*''' || Numbers in '''bold''' indicate graphs known to be optimal.
|-
|style="background-color: #bbffff; text-align: center;" | * || Optimal graphs.
|-
|style="background-color: beige; text-align: center;" | * || Optimal graphs found by E. Monakhova.
|-
|style="background-color: #66cc66; text-align: center;" | * || Graphs found by H. Macbeth, J. Šiagiová, J. Širáň and T. Vetrík.
|-
|style="background-color: magenta; text-align: center;" | * || Graphs found by R. Dougherty and V. Faber and independently for d=6 by E. Monakhova.
|-
|style="background-color: #81BEF7; text-align: center;" | * || Graphs found by B. McKay.
|-
|style="background-color: #66ff66; text-align: center;" | * || Graphs found by R. Lewis.
|-
|style="background-color: #CCFF00; text-align: center;" | * || Graphs found by R. Lewis and independently by R. Feria-Puron, H. Pérez-Rosés and J. Ryan.
|-
|style="background-color: yellow; text-align: center;" | * || Graphs found by R. Feria-Puron, H. Pérez-Rosés and J. Ryan.
|-
|style="background-color: orange; text-align: center;" | * || Graphs found by D. Bevan, G. Erskine and R. Lewis.
|-
|style="background-color: #cccccc; text-align: center;" | * || Graphs found by O. Monakhov and E. Monakhova.

|}
</center>

===Table of the lowest upper bounds known at present, and the percentage of the order of the largest known graphs===

<center>
{| border="1"
| '''<math>d</math>\<math>k</math>'''|| '''2''' || '''3''' ||  '''4'''|| '''5''' ||  '''6''' || '''7''' ||  '''8''' ||  '''9''' ||  '''10''' ||  '''11''' ||  '''12''' 
|-
|'''3'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|8
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|12
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|16
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|20
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|24
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|28
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|32
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|36
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|44
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|48
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|40
|-
|'''100%'''
|}
|-



|'''4'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|13
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|25
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|41
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|61
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|85
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|113
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|145
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|181
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|221
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|265
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|313
|-
|'''100%'''
|}
|-



|'''5'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|16
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|36
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|64
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|100
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|144
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|196
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|256
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|324
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|400
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|484
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|576
|-
|'''100%'''
|}
|-



|'''6'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|21
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|55
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|117
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|203
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|333
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|515
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|737
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|1 027
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|1 393
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|1 815
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|2 329
|-
|'''100%'''
|}
|-



|'''7'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|26
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|76
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|160
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|308
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|536
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|828
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|1 232
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|1 764
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|2 392
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|3 608
|-
|88%
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|4 672
|-
|89%
|}
|-



|'''8'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|35
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|104
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|248
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|528
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|984
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|1 712
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|3 649
|-
|76%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|5 641
|-
|76%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|8 361
|-
|76%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|11 969
|-
|76%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|16 641
|-
|75%
|}
|-



|'''9'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|42
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|130
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|320
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|700
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|1 416
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|3 530
|-
|72%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|5 890
|-
|73%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|9 290
|-
|73%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|14 002
|-
|74%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|20 330
|-
|74%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|28 610
|-
|74%
|}
|-



|'''10'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|51
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|177
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|681
|-
|67%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|1 683
|-
|65%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|3 653
|-
|65%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|7 183
|-
|63%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|13 073
|-
|63%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|22 363
|-
|63%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|36 365
|-
|63%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|56 695
|-
|63%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|85 305
|-
|62%
|}
|-



|'''11'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|56
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|210
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|912
|-
|63%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|2 364
|-
|60%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|5 336
|-
|60%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|10 836
|-
|61%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|20 256
|-
|61%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|35 436
|-
|61%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|58 728
|-
|61%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|93 060
|-
|61%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|142 000
|-
|61%
|}
|-



|'''12'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|67
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|275
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|1 289
|-
|64%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|3 653
|-
|58%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|8 989
|-
|56%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|19 825
|-
|54%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|40 081
|-
|53%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|75 517
|-
|53%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|134 245
|-
|52%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|227 305
|-
|52%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|369 305
|-
|52%
|}
|-



|'''13'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|80
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|312
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|1 666
|-
|58%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|4 942
|-
|54%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|12 642
|-
|49%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|28 814
|-
|51%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|59 906
|-
|51%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|115 598
|-
|50%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|209 762
|-
|51%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|361 550
|-
|51%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
|596610
|-
|50%
|}
|-



|'''14'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
|90
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
| 381
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 2 241
|-
|55%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 7 183
|-
|51%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 19 825
|-
|49%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 48 639
|-
|48%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 108 545
|-
|46%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 224 143
|-
|46%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 433 905
|-
|45%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 795 455
|-
|44%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 1 392 065
|-
|43%
|}
|-



|'''15'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
| 96
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
| 448
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 2 816
|-
|50%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 9 424
|-
|46%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 27 008
|-
|45%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 68 464
|-
|47%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 157 184
|-
|44%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 332 688
|-
|43%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 658 048
|-
|42%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 1 229 360
|-
|42%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 2 187 520
|-
|42%
|}
|-



|'''16'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
| 112
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 833
|-
|62%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 3 649
|-
|49%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 13 073
|-
|45%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 40 081
|-
|44%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 108 545
|-
|41%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 265 729
|-
|41%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 598 417
|-
|39%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 1 256 465
|-
|38%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 2 485 825
|-
|37%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 4 673 345
|-
|36%
|}
|-


|'''17'''
| align="center" |
{| border="2" style="background:rgb(180,180,255);" 
| 130
|-
|'''100%'''
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 978
|-
|0%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 4 482
|-
|0%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 16 722
|-
|39%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 53 154
|-
|38%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 148 626
|-
|39%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 374 274
|-
|36%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 864 146
|-
|37%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 1 854 882
|-
|36%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 3 742 290
|-
|36%
|}
| align="center" |
{| border="2" style="background:#ABCDEF;" 
| 7 159 170
|-
|35%
|}

|}
</center>

==References==
* D. Bevan, G. Erskine, and R. Lewis. Large circulant graphs of fixed diameter and arbitrary degree. [http://arxiv.org/abs/1506.04962 ArXiv] 
* R. Feria-Puron, J. Ryan, and H. Perez-Roses. Searching for Large Multi-Loop Networks. Electronic Notes in Discrete Mathematics, vol. 46 (2014), pp. 233-240. doi:10.1016/j.endm.2014.08.031. [http://www.sciencedirect.com/science/article/pii/S1571065314000328 Link to journal]
* R.R. Lewis. The Degree/Diameter Problem for Circulant Graphs of Degree 8 and 9. The Electronic Journal of Combinatorics, vol. 21(4) (2014), #P4.50. [http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i4p50 Link to journal]
* E.A. Monakhova, Synthesis of optimal Diophantine structures, Comput. Syst. Novosibirsk , 80 (1979), p.18--35. (in Russian).
* E. Monakhova, Optimal Triple Loop Networks with Given Transmission Delay: Topological Design and Routing, Inter. Network Optimization Conference, (INOC'2003), Evry/Paris, France, (2003), p.410--415. 
* E.A. Monakhova .  On synthesis of multidimensional circulant graphs of diameter two,  Bulletin of the Tomsk Polytechnic University.  323(2) (2013), p.25--28. (in Russian). [http://izvestiya.tpu.ru/en/archive/article.html?id=265621&journalId= Link to journal]