This is a table of all feasible parameter sets for 5-class Q-bipartite, not Q-antipodal association schemes up to 50,000 vertices. The definition of feasible is a parameter set satisfying integral eigenvalue multiplicities and pijk, the Krein conditions, the absolute bound, and the handshaking lemma.

The columns are as follows:
Parameters = a link to a file with all parameters,
∃ = ! if unique, n! if exactly n exist, " " if one example is known, + if more than one is known, - if it does not exist
v = the number of vertices
m1 = the multiplicity of the 1st eigenspace in the Q-polynomial ordering
Krein array = the formally dual notion of a Distance-Regular graph intersection array
multiplicities = the list of eigenvalues multiplicities in the Q-polynomial ordering
valencies = the list of valencies in the standard ordering with respect to the Q-polynomial ordering
2nd Q- lists whether another Q-polynomial ordering exists, note this other ordering will also have its own row in the table as well, unless it is identical.
P - lists whether there are one or two P-orderings
DRG - if the scheme is generated by one or two distance-regular graph, gives an intersection array for one of them. See [BCN] and [VKT] in the references for more details on distance-regular graphs
Quotient - The parameters of the (v,k,lambda,mu)-SRG that would be the quotient of the putative scheme. For more information on strongly-regular graphs, see the table of Andries Brouwer here.
Hyp - Denotes whether the putative scheme could arise as the extended Q-bipartite double of a 4-class primitive Q-polynomial scheme. The 4-class scheme would arise as a certain subscheme with half of the vertices of the original, one from each antipodal class. FS stands for this being feasible. It is possible for the Q-bipartite scheme to exist, have the subscheme be feasible, but not exist.

Acknowledgements: The construction of this table was supported in part by NSF grant DMS-1400281.
Special thanks to the following for suggestions/pointing out errors: William J. Martin

Reference List

Parameters v m1 Krein Array multiplicities valencies 2nd Q P DRG Quotient Hyp Comments
<252,9> + 252 9 {9,8,243/35,144/25,21/5; 1,72/35,81/25,24/5,9} 1,9,35,75,90,42 1,25,100,100,25,1 - 012345 {25,16,9,4,1;1,4,9,16,25} <126,25,8,4> FS J(10,5)
<312,13> + 312 13 {13,12,169/15,26/5,13/5; 1,26/15,39/5,52/5,13} 1,13,90,130,65,13 1,30,30,125,125,1 052341 - <156,30,4,6> Moorhouse-W q=5
<512,10> + 512 10 {10,9,8,7,6; 1,2,3,4,10} 1,10,45,120,210,126 1,45,210,210,45,1 - 012345 {45,28,15,6,1;1,6,15,28,45} <256,45,16,6> FS Halved 10-cube
<576,21> ? 576 21 {21,20,18,21/2,27/7; 1,3,21/2,120/7,21} 1,21,140,240,147,27 1,42,245,245,42,1 - - <288,42,6,6>
<800,25> ? 800 25 {25,24,625/28,75/7,25/7; 1,75/28,100/7,150/7,25} 1,25,224,350,175,25 1,56,56,343,343,1 052341 - <400,56,6,8> GQ(7)?
<1640,41> + 1640 41 {41,40,1681/45,164/9,41/9; 1,164/45,205/9,328/9,41} 1,41,450,738,369,41 1,90,729,729,90,1 052341 - <820,90,8,10> FS Moorhouse-W q=9
<2000,25> ? 2000 25 {25,24,625/27,50/3,25/9; 1,50/27,25/3,200/9,25} 1,25,324,900,675,75 1,270,729,729,270,1 - - <1000,270,80,70>
<2400,22> ? 2400 22 {22,21,20,88/5,32/11; 1,2,22/5,210/11,22} 1,22,231,1050,968,128 1,352,847,847,352,1 - - <1200,352,120,96>
<2928,61> ? 2928 61 {61,60,3721/66,305/11,61/11; 1,305/66,366/11,610/11,61} 1,61,792,1342,671,61 1,132,132,1331,1331,1 052341 - <1464,132,10,12> GQ(11)?
<4760,85> + 4760 85 {85,84,7225/91,510/13,85/13; 1,510/91,595/13,1020/13,85} 1,85,1274,2210,1105,85 1,182,182,2197,2197,1 052341 - <2380,182,12,14> Moorhouse-W q=13
<6272,77> - 6272 77 {77,76,147/2,35,7; 1,7/2,42,70,77} 1,77,1672,2926,1463,133 1,209,2926,2926,209,1 052341 042315 {209,196,105,14,1;1,14,105,196,209} <3136,209,12,14> BCN Thm 4.4.4 [BCN]
<6272,133> - 6272 133 {133,132,245/2,63,7; 1,21/2,70,126,133} 1,133,1672,2926,1463,77 1,209,2926,2926,209,1 052341 012345 {209,196,105,14,1;1,14,105,196,209} <3136,209,12,14> BCN Thm 4.4.4 [BCN]
<7232,113> ? 7232 113 {113,112,12769/120,791/15,113/15; 1,791/120,904/15,1582/15,113} 1,113,1920,3390,1695,113 1,240,240,3375,3375,1 052341 - <3616,240,14,16> GQ(15)?
<10440,145> + 10440 145 {145,144,21025/153,1160/17,145/17; 1,1160/153,1305/17,2320/17,145} 1,145,2754,4930,2465,145 1,306,306,4913,4913,1 052341 - <5220,306,16,18> Moorhouse-W q=17
<10584,66> - 10584 66 {66,65,432/7,50,21; 1,30/7,16,45,66} 1,66,1001,3861,4290,1365 1,286,5005,5005,286,1 - 012345 {286,245,112,14,1;1,14,112,245,286} <5292,286,40,14> BCN Thm 4.4.4 [BCN]
<13664,61> ? 13664 61 {61,60,3721/63,122/3,427/27; 1,122/63,61/3,1220/27,61} 1,61,1890,5490,4941,1281 1,270,6561,6561,270,1 - - <6832,270,26,10>
<14480,181> ? 14480 181 {181,180,32761/190,1629/19,181/19; 1,1629/190,1810/19,3258/19,181} 1,181,3800,6878,3439,181 1,380,380,6859,6859,1 052341 - <7240,380,18,20> GQ(19)?
<16352,73> ? 16352 73 {73,72,5329/75,146/3,73/25; 1,146/75,73/3,1752/25,73} 1,73,2700,7884,5475,219 1,2100,6075,6075,2100,1 - - <8176,2100,560,532>
<19448,221> ? 19448 221 {221,220,48841/231,2210/21,221/21; 1,2210/231,2431/21,4420/21,221} 1,221,5082,9282,4641,221 1,462,462,9261,9261,1 052341 - <9724,462,20,22> GQ(21)?
<25440,265> ? 25440 265 {265,264,70225/276,2915/23,265/23; 1,2915/276,3180/23,5830/23,265} 1,265,6624,12190,6095,265 1,552,552,12167,12167,1 052341 - <12720,552,22,24> GQ(23)?
<26624,52> ? 26624 52 {52,51,1352/27,130/3,208/9; 1,52/27,26/3,260/9,52} 1,52,1377,7956,11934,5304 1,918,12393,12393,918,1 - - <13312,918,134,58>
<28160,190> - 28160 190 {190,189,2000/11,255/2,22; 1,90/11,125/2,168,190} 1,190,4389,12768,9690,1122 1,513,13566,13566,513,1 - 012345 {513,476,225,18,1;1,18,225,476,513} <14080,513,36,18> BCN Thm 4.4.4 [BCN]
<32552,313> + 32552 313 {313,312,97969/325,3756/25,313/25; 1,3756/325,4069/25,7512/25,313} 1,313,8450,15650,7825,313 1,650,15625,15625,650,1 052341 - <16276,650,24,26> FS Moorhouse-W q=25
<34400,43> ? 34400 43 {43,42,1849/45,344/9,215/9; 1,86/45,43/9,172/9,43} 1,43,945,8127,16254,9030 1,1890,15309,15309,1890,1 - - <17200,1890,350,190>
<37752,121> ? 37752 121 {121,120,14641/125,484/5,121/25; 1,484/125,121/5,2904/25,121} 1,121,3750,18150,15125,605 1,3250,15625,15625,3250,1 - - <18876,3250,624,546>
<40880,365> ? 40880 365 {365,364,133225/378,4745/27,365/27; 1,4745/378,5110/27,9490/27,365} 1,365,10584,19710,9855,365 1,756,756,19683,19683,1 052341 - <20440,756,26,28> GQ(27)?
<47040,116> ? 47040 116 {116,115,112,696/7,144/29; 1,4,116/7,3220/29,116} 1,116,3335,22540,20184,864 1,4176,19343,19343,4176,1 - - <23520,4176,840,720>
<49896,209> - 49896 209 {209,208,605/3,154,33; 1,22/3,55,176,209} 1,209,5928,21736,19019,3003 1,741,24206,24206,741,1 - 012345 {741,686,315,21,1;1,21,315,686,741} <24948,741,54,21> BCN Thm 4.4.4 [BCN]