Mixed tournaments

↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓
Tables	Set	Total	λ	No. of rounds	Combinations	Group order	Group	Structure	Tournament Schedule	Image	Status
2	3,3	6	2,2	10	20	60	psl(2,5)	Faces of the hemiicosahedron 2-(6,10,5,3,2)	Schedule		confirmed
3	3,3,1	7	1,1	7	140	336	sl(3,2)	(Projective plane of order 2) Triangular lattice(1,3) Biplane of order 2 2-(7,14,6,3,2)	Schedule		confirmed
2	3,4	7	1,2	7	35	168	psl(3,2) psl(2,7)	Fano plane Projective plane of order 2 S(2,3,7)	Schedule		confirmed
2	4,4	8	3,3	14	70			S(3,4,8)	Schedule		confirmed
3	2*4,1	9	3	9	315			Square lattice(3,0)	∀ a,b ∋ℤ3: (a±1,b±1) & (a,b±1)+(a±1,b) Schedule		confirmed
3	3,3,3	9	1,1,1	12	1680	432		Affine plane of order 3	Schedule		confirmed
2	3,6	9	1,5	12	84	432		Affine plane of order 3 S(2,3,9)	(see 3,3,3 above) Schedule		confirmed
2	4,5	9	3,5	18	126				Schedule		confirmed
4	3*3,1	10	2	10	2160			hemidodecahedron with face-centred wedge-shaped blocks 2-(10,30,9,3,2)	Schedule		confirmed
2	3,7	10	2,14	30	120	360		2-(10,30,9,3,2)	Schedule		confirmed
2	4,6	10	2,5	15	210	720		hemidodecahedron with edge-centred rhombic blocks	∀ a ∋ℤ5: (a,a+3,a+5.a+6),(a,a+1,a+2,a+8),(a+1,a+3,a+6,a+7) Schedule		confirmed
3	5,5,1	11	2,2	11	2772			2-(11,22,10,5,4)	Schedule		confirmed
2	5,6	11	2,3	11	462	660	psl(2,11)	Paley biplane biplane of order 3 2-(11,11,5,5,2)	(see 5,5,1 above) Schedule		confirmed
2	2*6	12	5	22	462			3-(12,22,11,6,2)	(5,6 above with a 12th player joining each 5) Schedule		confirmed
2	2*6	12	30	66	1848	95040	M12	S(5,6,12) The blocks are all clusters of vertices of the icosahedron shaped like any of these three:	Schedule		confirmed
2	6,6	12	30	132	924	95040	M12	S(5,6,12) The blocks are as for 2*6, and their complements.	Schedule		confirmed
3	2*6,1	13	5	13	6006			Triangular lattice(2,4) 2-(13,26,12,6,5)	∀ a ∋ℤ13: (a±1,a±3,a±9); (a±2,a±6,a±5) Schedule		confirmed
4	3*4,1	13	3	13	450450			Square lattice(3,2) 2-(13,39,12,4,3)	∀ a ∋ℤ13: (a±2,a±3); (a±1,a±5); (a±4,a±6) Schedule		confirmed
2	3,10	13	1,15	26	286	1560		S(2,3,13)		​	confirmed
2	4,9	13	1,12	13	715	5616	psl(3,3)	S(2,4,13) projective plane of order 3			confirmed
2	3,12	15	1,22	35	455			S(2,3,15)		​	confirmed
5	5*3	15	1	7	1401400			Kirkman's schoolgirls S(2,3,15)		​	confirmed
4	3*5,1	16	4	16	2018016			Colouring of K16 as three Clebsch graphs	Schedule		confirmed
2	4,4,4,4	16	1,1,1,1	20	63063000			Affine plane of order 4 (2,4,16)			confirmed
6	5*3,1	16	2	16	>109			Triangular lattice(4,4)		​	confirmed
2	6,10	16	2,6	16	8008			Menon design biplane of order 4		​	confirmed
5	4*4,1	17	3	17	1072071000			Square lattice(4,1)		​	confirmed
6	3*3,3*3,1	19	2	19	>1013			Triangular lattice(1,5) 2-(19,114,18,3,2)	∀ a ∋ℤ19: (a+1,a+7,a+11); (a+8,a+12,a+18); (a+4,a+6,a+9); (a+10,a+13,a+15); (a+2,a+3,a+14); (a+5,a+16,a+17); Schedule		confirmed
4	3*6,1	19	5	19	325909584			Triangular lattice(1,5) 2-(19,57,18,6,5)	∀ a ∋ℤ19: (a±1,a±7,a±8); (a±4,a±6,a±9); (a±2,a±3,a±5) Schedule		confirmed
2	3,16	19	1,40	57	969			S(2,3,19)		​	confirmed
2	9,10	19	4,5	19	92378				Schedule		confirmed
2	9,9,1	19	4,5	19	923780				Schedule		confirmed
2	10,10	20	9	38	92378			3-(20,38,19,10,4)	Schedule		confirmed
2	3,18	21	1,51	70	1330			S(2,3,21)		​	confirmed
2	5,16	21	1,12	21	20349	40320	psl(3,4):S6	projective plane of order 4		​	confirmed
2	7,15	22	2,10	22	170544			biplane of order 5		​	confirmed
3	11,11,1	23	5,5,5,5	23	16224936				Schedule		confirmed
2	11,12	23	5,6	23	1352078				Schedule		confirmed
2	12,12	24	11	46	2704156			3-(24,46,23,12,5)	Schedule		confirmed
2	3,22	25	1,77	100	2300			S(2,3,25)		​	confirmed
5	4*6,1	25	5	25	>1013			Triangular lattice(5,5)		​	confirmed
2	4,21	25	1,35	50	12650			S(2,4,25)		​	confirmed
2	5,20	25	1,19	30	53130			affine plane of order 5 S(2,5,25)		​	confirmed
9	8*3,1	25	1	25	>1018			Triangular lattice(5,5)		​	confirmed
2	9,28	37	2,21	37	124403620			Biplane of order 7		​	confirmed
2	11,45	56	2,36	56	>1011			biplane of order 9		​	confirmed
2	13,66	79	2,55	79	>1014			Biplane of order 11		​	confirmed
2	6,10	16	1,3	8	8008					​	does not exist
3	3,3,4	10	2,2,4	30	4200					​	unknown
2	3,8	11	3,28	55	165					​	unknown
2	4,7	11	6,21	55	330					​	unknown
2	3,9	12	2,24	44	220					​	unknown
2	4,8	12	3,14	33	495					​	unknown
3	5,6,1	12	20,30	132	5544	95040	M12	S(5,6,12)		​	unknown
4	3,3,3,4	13	1,1,1,2	26	1201200					​	unknown
2	3,3,7	13	1,7	26	34320					​	unknown
3	3,4,6	13	1,2,5	26	60060					​	unknown
3	4,4,5	13	3,3,4	39	90090					​	unknown
3	6,6,1	13	5,5	26	12012					​	unknown
2	6,7	13	5,7	26	1716			2-(13,26,12,6,5)		​	unknown
2	2*7	14	12	26	1716			2-(14,52,26,7,12)		​	unknown
2	8,9	17	7,9	34	24310					​	unknown
2	10,11	21	9,11	42	352716					​	unknown
4	5,5,5,6	21	2,2,2,3	42	>1010					​	unknown
2	5,6,10	21	2,3,9	42	162954792					​	unknown
2	6,15	21	3,21	42	54264					​	unknown
2	9,12	21	6,11	35	293930					​	unknown
5	4,4,4,4,9	25	1,1,1,1,6	50	>1014					​	unknown
2	7,8	15	3,4	15	6435			2-(15,15,7,7,3)		​	conjectured
n	n*2	2n	n*1	2n-1	(2n)!/(n!sn)	(2n)!	S2n	K2n			confirmed
n+1	n*2+1	2n+1	n*1	2n	(2n)!/(n!sn)	(2n+1)!	S2n+1	K2n+1			confirmed
↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓	↑ ↓