| No. of vertices | Intersection Array | Graph |
| $8$ | $\{3,2,1;1,2,3\}$ | $\text{3-cube }Q_3 \cong H(3,2)$ |
| $10$ | $\{4,3,1; 1,3,4\}$ | $K_{5,5}-I$ |
| $12$ | $\{5,4,1; 1,4,5\}$ | $K_{6,6}-I$ |
| $12$ | $\{5,2,1;1,2,5\}$ | $\text{Icosahedron}$ |
| $14$ | $\{3,2,2;1,1,3\}$ | $\text{Heawood graph (Incidence graph of }PG(2,2))$ |
| $14$ | $\{4,3,2;1,2,4\}$ | $\text{Distance-3 graph of Heawood graph (Non-incidence graph of }PG(2,2)\text{)}$ |
| $14$ | $\{6,5,1; 1,5,6\}$ | $K_{7,7}-I$ |
| $15$ | $\{4,2,1;1,1,4\}$ | $\text{Line graph of Petersen graph}$ |
| $16$ | $\{7,6,1; 1,6,7\}$ | $K_{8,8}-I$ |
| $18$ | $\{8,7,1; 1,7,8\}$ | $K_{9,9}-I$ |
| $20$ | $\{9,4,1;1,4,9\}$ | $J(6,3)$ |
| $20$ | $\{9,8,1; 1,8,9\}$ | $K_{10,10}-I$ |
| $21$ | $\{4,2,2;1,1,2\}$ | $\text{Line graph of Heawood graph (Flag graph of }PG(2,2)\text{)}$ |
| $22$ | $\{5,4,3;1,2,5\}$ | $\text{Incidence graph of biplane on 11 points}$ |
| $22$ | $\{6,5,3;1,3,6\}$ | $\text{Incidence graph of }(11,6,3)\text{-design}$ |
| $22$ | $\{10,9,1; 1,9,10\}$ | $K_{11,11}-I$ |
| $24$ | $\{7,4,1;1,2,7\}$ | $\text{Klein graph}$ |
| $24$ | $\{11,10,1; 1,10,11\}$ | $K_{12,12}-I$ |
| $26$ | $\{4,3,3;1,1,4\}$ | $\text{Incidence graph of }PG(2,3)$ |
| $26$ | $\{9,8,3;1,6,9\}$ | $\text{Incidence graph of }(13,9,3)\text{-design}$ |
| $26$ | $\{12,11,1; 1,11,12\}$ | $K_{13,13}-I$ |
| $27$ | $\{6,4,2;1,2,3\}$ | $H(3,3)$ |
| $27$ | $\{8,6,1;1,3,8\}$ | $GQ(2,4)\text{ minus spread (2 graphs)}$ |
| $28$ | $\{13,16,1;1,6,13\}$ | $\text{Taylor graph from }P_{13}$ |
| $28$ | $\{13,12,1; 1,12,13\}$ | $K_{14,14}-I$ |
| $30$ | $\{7,6,4;1,3,7\}$ | $\text{Incidence graph of }PG(3,2)$ |
| $30$ | $\{7,6,4;1,3,7\}$ | $\text{Incidence graphs of Hadamard (15,7,3)-designs}$ |
| $30$ | $\{8,7,4;1,4,8\}$ | $\text{Incidence graph of complement of }PG(3,2)$ |
| $30$ | $\{8,7,4;1,4,8\}$ | $\text{Incidence graphs of }(15,8,4)\text{-designs }(N=4)$ |
| $30$ | $\{14,13,1; 1,13,14\}$ | $K_{15,15}-I$ |
| $32$ | $\{6,5,4;1,2,6\}$ | $\text{Folded 6-cube}$ |
| $32$ | $\{6,5,4;1,2,6\}$ | $\text{Incidence graphs of biplanes on 16 points}$ |
| $32$ | $\{8,7,4;1,4,8\}$ | $\text{Incidence graphs of }(16,10,6)\text{-designs}$ |
| $32$ | $\{15,6,1; 1,6,15\}$ | $\text{Taylor graph from }J(6,2) \cong \text{ Halved 6-cube}$ |
| $32$ | $\{15,8,1; 1,8,15\}$ | $\text{Taylor graph from }K(6,2)$ |
| $32$ | $\{15,14,1; 1,14,15\}$ | $K_{16,16}-I$ |
| $34$ | $\{16,15,1; 1,15,16\}$ | $K_{17,17}-I$ |
| $35$ | $\{4,3,3;1,1,2\}$ | $\text{Odd graph }O_4$ |
| $35$ | $\{12,6,2;1,4,9\}$ | $J(7,3)$ |
| $36$ | $\{5,4,2;1,1,4\}$ | $\text{Sylvester graph}$ |
| $36$ | $\{17,8,1;1,8,17\}$ | $\text{Taylor graph from }P_{17}$ |
| $38$ | $\{9,8,5;1,4,9\}$ | $\text{Incidence graphs of Hadamard (19,9,4)-designs}$ |
| $42$ | $\{13,8,1;1,4,13\}$ | $\text{Coolsaet-Degraer 3-cover of }K_{14}$ |
| $42$ | $\{5,4,4;1,1,5\}$ | $\text{Incidence graph of PG(2,4)}$ |
| $42$ | $\{13,8,1;1,4,13\}$ | $\text{Symplectic 3-cover of }K_{14}$ |
| $42$ | $\{6,5,1;1,1,6\}$ | $2^{nd}\text{ subconstituent of Hoffman-Singleton graph}$ |
| $51$ | $\{16,10,1;1,5,16\}$ | $\text{Symplectic 3-cover of }K_{17}$ |
| $52$ | $\{6,3,3;1,1,2\}$ | $\text{Flag graph of }PG(2,3)$ |
| $56$ | $\{15,8,3;1,4,9\}$ | $J(8,3)$ |
| $56$ | $\{27,10,1;1,10,27\}$ | $\text{Gosset graph}$ |
| $56$ | $\{27,16,1;1,16,27\}$ | $\text{Distance-2 graph of Gosset graph}$ |
| $57$ | $\{6,5,2;1,1,3\}$ | $\text{Perkel graph}$ |
| $60$ | $\{11,8,1;1,2,11\}$ | $\text{Symplectic 5-cover of }K_{12}$ |
| $62$ | $\{6,5,5;1,1,6\}$ | $\text{Incidence graph of }PG(2,5)$ |
| $62$ | $\{15,14,8;1,7,15\}$ | $\text{Incidence graph of }PG(4,2)$ |
| $63$ | $\{6,4,4;1,1,3\}$ | $\text{Point graphs of }GH(2,2) \text{ and its dual}$ |
| $63$ | $\{8,6,1;1,1,8\}$ | $\text{Symplectic 7-cover of }K_9$ |
| $64$ | $\{9,6,3;1,2,3\}$ | $H(3,4)$ |
| $64$ | $\{7,6,5;1,2,3\}$ | $\text{Folded 7-cube}$ |
| $64$ | $\{21,10,3;1,6,15\}$ | $\text{Halved 7-cube}$ |
| $65$ | $\{10,6,4;1,2,5\}$ | $\text{Hall graph}$ |
| $68$ | $\{12,10,3;1,3,8\}$ | $\text{Doro graph}$ |
| $80$ | $\{13,12,9;1,4,13\}$ | $\text{Incidence graph of }PG(3,3)$ |
| $84$ | $\{18,10,4;1,4,9\}$ | $J(9,3)$ |
| $85$ | $\{16,12,1;1,3,16\}$ | $\text{Symplectic 5-cover of }K_{17}$ |
| $105$ | $\{8,4,4;1,1,2\}$ | $\text{Flag graph of }PG(2,4)$ |
| $114$ | $\{8,7,7;1,1,8\}$ | $\text{Incidence graph of }PG(2,7)$ |
| $120$ | $\{21,12,5;1,4,9\}$ | $J(10,3)$ |
| $125$ | $\{12,8,4;1,2,3\}$ | $H(3,5)$ |
| $146$ | $\{9,8,8;1,1,9\}$ | $\text{Incidence graph of }PG(2,8)$ |
| $175$ | $\{12,6,5;1,1,4\}$ | $\text{Line graph of Hoffman-Singleton graph}$ |
| $182$ | $\{10,9,9;1,1,10\}$ | $\text{Incidence graph of }PG(2,9)$ |
| $186$ | $\{10,5,5;1,1,2\}$ | $\text{Flag graph of }PG(2,5)$ |
| $208$ | $\{12,10,5;1,1,8\}$ | $\text{Unitary graph from P}\Gamma \text{U(3,4)}$ |
| $266$ | $\{12,11,11;1,1,12\}$ | $\text{Incidence graph of }PG(2,11)$ |
| $288$ | $\{66,65,36;1,30,66\}$ | $\text{Incidence graphs of Leonard semibiplanes}$ |
| $352$ | $\{175,102,1;1,102,175\}$ | $\text{Taylor graph from Higman-Sims group (a)}$ |
| $352$ | $\{175,72,1;1,72,175\}$ | $\text{Taylor graph from Higman-Sims group (b)}$ |
| $352$ | $\{50,49,36;1,14,50\}$ | $\text{Incidence graph of Higman's symmetric design}$ |
| $364$ | $\{12,9,9;1,1,4\}$ | $\text{Point graph of }GH(3,3)$ |
| $506$ | $\{15,14,12;1,1,9\}$ | $\text{Truncated Witt graph}$ |
| $512$ | $\{21,20,16;1,2,12\}$ | $\text{Coset graph of doubly truncated binary Golay code}$ |
| $525$ | $\{20,18,6;1,1,15\}$ | $\text{Unitary graph from P}\Gamma \text{U(3,5)}$ |
| $552$ | $\{275,112,1;1,112,275\}$ | $\text{Taylor graph from }Co_3 \text{ (a)}$ |
| $552$ | $\{275,162,1;1,162,275\}$ | $\text{Taylor graph from }Co_3 \text{ (b)}$ |
| $672$ | $\{110,81,12;1,18,90\}$ | $\text{Moscow-Soicher graph}$ |
| $729$ | $\{24,22,20;1,2,12\}$ | $\text{Coset graph of extended ternary Golay code}$ |
| $759$ | $\{30,28,24;1,3,15\}$ | $\text{Witt graph}$ |
| $1024$ | $\{22,21,20;1,2,6\}$ | $\text{Coset graph of truncated binary Golay code}$ |
| $1024$ | $\{231,160,6;1,48,210\}$ | $\text{Distance-2 graph of coset graph of truncated binary Golay code}$ |
| $1024$ | $\{33,30,15;1,2,15\}$ | $\text{Shi-Krotov-Solé graph}$ |
| $1395$ | $\{98,72,32;1,9,49\}$ | $\text{Grassmann graph }J_2(6,3)$ |