BCN tables

In [BCN] tables for feasible parameter sets for distance-regular graphs on at most 4096 vertices were given. The corresponding tables for the case of bipartite graphs of diameter 4 were given in the PDF file with additions and corrections.

On this page we give this material in a machine readable form.

Files are IA3P, IA4A, IA4B, IA4C, IA4P, IA5A, IA5B, IA5C, IA5P, IA6A, IA6B, IA6C, IA6P, IA7A, IA7C, IA7P, IA8, IA9, IA10, IA11, IA12, IA13 where the suffixes P, A, B, C stand for primitive, antipodal, bipartite and both antipodal and bipartite.

Number of intersection arrays:
IA3P IA4A IA4B IA4C IA4P IA5A IA5B IA5C IA5P IA6A IA6B IA6C IA6P IA7A IA7C IA7P IA8 IA9 IA10 IA11 IA12 IA13
187 179 160 847 46 12 5 33 11 6 5 1 9 1 5 2 3 2 1 2 1 1

For several of these arrays it has been shown that no corresponding graph exists. It you meet such an array, please write to aeb@cwi.nl and give the array, and the reason why it does not exist, preferably with a reference to the corresponding publication, and I will add that data here.

The following antipodal arrays with d=4 
i(45,32,9,1; 1,9,32,45)
i(45,32,15,1; 1,3,32,45)
i(56,45,18,1; 1,6,45,56)
i(56,45,21,1; 1,3,45,56)
i(81,56,24,1; 1,3,56,81)
i(96,75,28,1; 1,4,75,96)
i(115,96,32,1; 1,8,96,115)
i(115,96,35,1; 1,5,96,115)
i(115,96,36,1; 1,4,96,115)
i(117,80,27,1; 1,9,80,117)
i(117,80,30,1; 1,6,80,117)
i(117,80,32,1; 1,4,80,117)
i(175,144,25,1; 1,25,144,175)
i(176,135,40,1; 1,8,135,176)
i(189,128,27,1; 1,27,128,189)
i(189,128,45,1; 1,9,128,189)
i(204,175,40,1; 1,20,175,204)
i(204,175,45,1; 1,15,175,204)
i(261,176,54,1; 1,18,176,261)
i(414,350,45,1; 1,45,350,414)
have been ruled out in
A. Jurišić and J. H. Koolen, Nonexistence of some antipodal distance-regular graphs of diameter four, Europ. J. Comb. 21 (2000) 1039-1046.
Michael Lang notes that the five arrays 
i(21,20,9,3,1; 1,3,9,20,21)
i(36,35,16,4,1; 1,4,16,35,36)
i(55,54,25,5,1; 1,5,25,54,55)
i(78,77,36,6,1; 1,6,36,77,78)
i(105,104,49,7,1; 1,7,49,104,105)
from IA5A (and, more generally, antipodal 2-covers with d=5 and c=(1,m,m2,2m2+m−1,2m2+m) with m > 1) have been ruled out in
K. Coolsaet, A. Jurišić and J. H. Koolen, On triangle-free distance-regular graphs with an eigenvalue multiplicity equal to the valency, European J. of Combinatorics 29 (2008) 1186-1199.
Jason Galazidis notes that the two arrays 
i(56,45,12,1;1,12,45,56)
i(36,35,27,6;1,9,30,36)
are ruled out since the distance 3-or-4 (resp. 1-or-4) graph would be a srg(324,57,0,12), and there is none (Kaski & Östergård).
Mario Huang notes that the two arrays 
i(36,35,33,3; 1,3,33,36)
i(88,87,77,4; 1,11,84,88)
are ruled out since the halved graph would be a nonexistent srg.

Extended tables

Somewhat larger tables (with parameters for graphs of diameter 4 or 5 on at most 16384 vertices) are given in the file IA4a, IA5a. Somewhat larger tables (with parameters for graphs of diameter at least 6 on at most 65536 vertices) are given in the files IA6b, IA7b, IA8b, IA9b, IA10b, IA11b, IA12b, IA13b, IA14b, IA15b, IA16b, IA17b.

Number of intersection arrays:
IA4a IA5a IA6b IA7b IA8b IA9b IA10b IA11b IA12b IA13b IA14b IA15b IA16b IA17b
5084 111 43 22 14 4 2 2 1 2 1 2 1 1
(5290 in all).