# MAPLE.  June 3, 2006.
#
# 3-class primitive Q-polynomial association scheme
# defined on blocks of the unique 5-(24,8,1) design.
d := 3;
v := [ 1,  280,  448,  30 ];
verts := 759;


Q := matrix([
[1 ,   23   ,   252 ,   483 ],
[1 ,  23/4  ,  18/5 ,-207/20],
[1 ,  -23/8 ,  -27/4,   69/8],
[1 ,  -23/2 ,  294/5,-483/10]
]):

# Tridiagonal matrix L = L1-star can be used to obtain Q (and
# then all parameters) from just the cosines.
L := matrix([
[ 0 ,    23    ,     0    ,      0   ],
[ 1 ,   23/44  ,  945/44  ,      0   ],
[ 0 ,  345/176 ,  529/440 ,  1587/80 ],
[ 0 ,     0    ,  207/20  ,   253/20 ]
]):


        [0    280      0     0]
        [                     ]
        [1    140    136     3]
L_1  =  [                     ]
        [0     85    180    15]
        [                     ]
        [0     28    224    28]

        [0      0    448     0]
        [                     ]
        [0    136    288    24]
L_2  =  [                     ]
        [1    180    252    15]
        [                     ]
        [0    224    224     0]

        [0     0     0    30]
        [                   ]
        [0     3    24     3]
L_3  =  [                   ]
        [0    15    15     0]
        [                   ]
        [1    28     0     1]

      [1    280    448     30]
      [                      ]
      [1     70    -56    -15]
P =   [                      ]
      [1      4    -12      7]
      [                      ]
      [1     -6      8     -3]

      [1     23       252     483 ]
      [                           ]
      [                       -207]
      [1    23/4     18/5     ----]
      [                        20 ]
 Q  = [                           ]
      [1    -23/8    -27/4    69/8]
      [                           ]
      [                       -483]
      [1    -23/2    294/5    ----]
      [                        10 ]

        [0    23      0      0  ]
        [                       ]
        [     23     945        ]
        [1    --     ---     0  ]
        [     44     44         ]
        [                       ]
Ls1  =  [     345    529    1587]
        [0    ---    ---    ----]
        [     176    440     80 ]
        [                       ]
        [            207    253 ]
        [0     0     ---    --- ]
        [            20     20  ]

        [0     0      252        0  ]
        [                           ]
        [     945     1449     4347 ]
        [0    ---     ----     ---- ]
        [     44      110       20  ]
        [                           ]
Ls2  =  [     529    126393    26979]
        [1    ---    ------    -----]
        [     440     1100      200 ]
        [                           ]
        [     207     3519     17127]
        [0    ---     ----     -----]
        [     20       50       100 ]

        [0     0        0       483  ]
        [                            ]
        [             4347      5313 ]
        [0     0      ----      ---- ]
        [              20        20  ]
        [                            ]
Ls3  =  [     1587    26979    131307]
        [0    ----    -----    ------]
        [      80      200      400  ]
        [                            ]
        [     253     17127     7452 ]
        [1    ---     -----     ---- ]
        [     20       100       25  ]