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  v k λ μ rf sgcomments
+ 53 26 12 13 3.14026 –4.14026 Paley(53); 2-graph\*
! 55 18 9 4 710 –244 Triangular graph T(11)
    36 21 28 144 –810  
! 56 10 0 2 235 –420 Sims-Gewirtz graph; L3(4).22 / Alt(6).22; unique by Gewirtz; Cossidente-Penttila hemisystem in PG(3,32)
    45 36 36 320 –335 Witt: intersection-2 graph of a quasisymmetric 2-(21,6,4) design with intersection numbers 0, 2
- 56 22 3 12 148 –107 Krein2; Absolute bound
    33 22 15 97 –248 Krein1; Absolute bound
- 57 14 1 4 238 –518 Wilbrink-Brouwer
    42 31 30 418 –338  
+ 57 24 11 9 518 –338 S(2,3,19)
    32 16 20 238 –618  
- 57 28 13 14 3.27528 –4.27528 Conf
+ 61 30 14 15 3.40530 –4.40530 Paley(61); Martin-Williford; 2-graph\*
- 63 22 1 11 155 –117 Krein2; Absolute bound
    40 28 20 107 –255 Krein1; Absolute bound
+ 63 30 13 15 335 –527 intersection-8 graph of a quasisymmetric 2-(36,16,12) design with intersection numbers 6, 8; O(7,2) Sp(6,2); pg(6,4,3); 2-graph\*
    32 16 16 427 –435 S(2,4,28); intersection-6 graph of a quasisymmetric 2-(28,12,11) design with intersection numbers 4, 6; NU(3,3); 2-graph\*
! 64 14 6 2 614 –249 82; from a partial spread of 3-spaces: projective binary [14,6] code with weights 4, 8
    49 36 42 149 –714 OA(8,7)
167! 64 18 2 6 245 –618 complete enumeration by Haemers & Spence; GQ(3,5); from a hyperoval: projective 4-ary [6,3] code with weights 4, 6; Momihara: projective binary [18,6] code with weights 8, 12
    45 32 30 518 –345  
- 64 21 0 10 156 –117 Krein2; Absolute bound
    42 30 22 107 –256 Krein1; Absolute bound
+ 64 21 8 6 521 –342 OA(8,3); Bilin2x3(2); vanLint-Schrijver(1); from a Baer subplane: projective 4-ary [7,3] code with weights 4, 6; Brouwer(q=2,d=2,e=3,+); from a partial spread of 3-spaces: projective binary [21,6] code with weights 8, 12
    42 26 30 242 –621 OA(8,6); vanLint-Schrijver(2); Momihara
+ 64 27 10 12 336 –527 Mesner; from a unital: projective 4-ary [9,3] code with weights 6, 8; VO–(6,2) affine polar graph; RSHCD–; 2-graph
    36 20 20 427 –436 from 2-(8,2,1) with 1-factor Fickus et al.; 2-graph
+ 64 28 12 12 428 –435 OA(8,4); Wallis (AR(2,2)+S(2,2,8)); from a partial spread of 3-spaces: projective binary [28,6] code with weights 12, 16; RSHCD+; 2-graph
    35 18 20 335 –528 OA(8,5); Wallis2 (AR(2,2)+S(2,2,8)); Goethals-Seidel(2,7); VO+(6,2) affine polar graph; 2-graph
- 64 30 18 10 108 –255 Absolute bound
    33 12 22 155 –118 Absolute bound
+ 65 32 15 16 3.53132 –4.53132 Gritsenko; 2-graph\*
! 66 20 10 4 811 –254 Triangular graph T(12)
    45 28 36 154 –911 pg(5,8,4) does not exist (Lam et al.)
? 69 20 7 5 523 –345  
    48 32 36 245 –623 S(2,6,46) does not exist
- 69 34 16 17 3.65334 –4.65334 Conf
+ 70 27 12 9 620 –349 S(2,3,21)
    42 23 28 249 –720 pg(6,6,4)?
+ 73 36 17 18 3.77236 –4.77236 Paley(73); 2-graph\*
- 75 32 10 16 256 –818 Azarija-Marc
    42 25 21 718 –356  
- 76 21 2 7 256 –719 Haemers
    54 39 36 619 –356  
- 76 30 8 14 257 –818 Bondarenko, Prymak & Radchenko
    45 28 24 718 –357  
- 76 35 18 14 719 –356  
    40 18 24 256 –819 no 2-graph\*
! 77 16 0 4 255 –621 S(3,6,22); M22/24:Sym(6); Mesner; unique by Brouwer; intersection-6 graph of a quasisymmetric 2-(56,16,6) design with intersection numbers 4, 6
    60 47 45 521 –355 Witt 3-(22,6,1): intersection-2 graph of a quasisymmetric 2-(22,6,5) design with intersection numbers 0, 2
- 77 38 18 19 3.88738 –4.88738 Conf
! 78 22 11 4 912 –265 Triangular graph T(13)
    55 36 45 165 –1012  
! 81 16 7 2 716 –264 92; vanLint-Schrijver(1); Brouwer(q=3,d=2,e=2,+); from a partial spread: projective ternary [8,4] code with weights 3, 6
    64 49 56 164 –816 OA(9,8); vanLint-Schrijver(4)
! 81 20 1 6 260 –720 Mesner; unique by Brouwer & Haemers; VO–(4,3) affine polar graph; projective ternary [10,4] code with weights 6, 9
    60 45 42 620 –360  
+ 81 24 9 6 624 –356 OA(9,3); Wallis (AR(3,1)+S(2,3,9)); VNO+(4,3) affine polar graph; from a partial spread: projective ternary [12,4] code with weights 6, 9
    56 37 42 256 –724 OA(9,7)
+ 81 30 9 12 350 –630 Mesner; pg(5,5,2) - van Lint & Schrijver; VNO–(4,3) affine polar graph; Hamada-Helleseth: projective ternary [15,4] code with weights 9, 12
    50 31 30 530 –450  
+ 81 32 13 12 532 –448 OA(9,4); Bilin2x2(3); vanLint-Schrijver(2); Wallis2 (AR(3,1)+S(2,3,9)); VO+(4,3) affine polar graph; from a partial spread: projective ternary [16,4] code with weights 9, 12
    48 27 30 348 –632 OA(9,6); vanLint-Schrijver(3)
- 81 40 13 26 172 –148 Absolute bound
    40 25 14 138 –272 Absolute bound
+ 81 40 19 20 440 –540 Paley(81); OA(9,5); 2-graph\*
+ 82 36 15 16 441 –540 switch OA(9,5)+*; 2-graph
    45 24 25 440 –541 S(2,5,41); 2-graph
- 85 14 3 2 434 –350 Shpectorov-Zhao
    70 57 60 250 –534  
+ 85 20 3 5 350 –534 O(5,4) Sp(4,4); GQ(4,4)
    64 48 48 434 –450  
? 85 30 11 10 534 –450  
    54 33 36 350 –634 S(2,6,51)?
? 85 42 20 21 4.11042 –5.11042 2-graph\*?
? 88 27 6 9 355 –632  
    60 41 40 532 –455  
+ 89 44 21 22 4.21744 –5.21744 Paley(89); Martin-Williford; 2-graph\*
! 91 24 12 4 1013 –277 Triangular graph T(14)
    66 45 55 177 –1113 pg(6,10,5)?
- 93 46 22 23 4.32246 –5.32246 Conf
- 95 40 12 20 275 –1019 Azarija-Marc
    54 33 27 919 –375  
+ 96 19 2 4 357 –538 Haemers(4); Muzychuk S6 (n=4,d=2); Brouwer-Koolen-Klin; Golemac et al.
    76 60 60 438 –457  
+ 96 20 4 4 445 –450 Wallis (AR(4,1)+S(2,2,6)); GQ(5,3); Brouwer-Koolen-Klin; Golemac et al.
    75 58 60 350 –545  
? 96 35 10 14 363 –732 pg(5,6,2)?
    60 38 36 632 –463  
- 96 38 10 18 276 –1019 Degraer
    57 36 30 919 –376  
- 96 45 24 18 920 –375  
    50 22 30 275 –1020 no 2-graph\*
+ 97 48 23 24 4.42448 –5.42448 Paley(97); 2-graph\*
? 99 14 1 2 354 –444  
    84 71 72 344 –454  
? 99 42 21 15 921 –377  
    56 28 36 277 –1021  
+ 99 48 22 24 454 –644 pg(8,5,4) does not exist (Lam et al.); 2-graph\*
    50 25 25 544 –554 S(2,5,45); 2-graph\*
! 100 18 8 2 818 –281 102
    81 64 72 181 –918  
! 100 22 0 6 277 –822 HS.2 / M22.2 - Mesner; Higman-Sims; unique by Gewirtz; q222=0
    77 60 56 722 –377 q111=0
+ 100 27 10 6 727 –372 OA(10,3)
    72 50 56 272 –827 OA(10,8)?
? 100 33 8 12 366 –733  
    66 44 42 633 –466  
+ 100 33 14 9 824 –375 S(2,3,25)
    66 41 48 275 –924  
- 100 33 18 7 1311 –288 Absolute bound
    66 39 52 188 –1411 Absolute bound
+ 100 36 14 12 636 –463 J2.2 / U3(3).2 - Hall-Janko; OA(10,4)
    63 38 42 363 –736 OA(10,7)?
+ 100 44 18 20 455 –644 Jørgensen-Klin; RSHCD–; 2-graph
    55 30 30 544 –555 2-graph
+ 100 45 20 20 545 –554 OA(10,5)?; RSHCD+; 2-graph
    54 28 30 454 –645 OA(10,6)?; 2-graph

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