There are 36 tiles for {2,8,9,16}:

T1 = {{0, 17, 20, 23, 28, 29, 40, 48, 53, 59, 65, 68, 76, 88, 89, 95,
    96, 101, 116, 124, 125, 131, 136, 137}, {0, 17, 24, 25, 30, 36,
    37, 45, 60, 65, 66, 72, 73, 85, 93, 96, 102, 108, 113, 121, 132,
    133, 138, 141}, {0, 19, 20, 24, 25, 28, 31, 48, 55, 61, 67, 68,
    72, 76, 91, 96, 97, 103, 116, 120, 124, 127, 133, 139}, {0, 19,
    20, 25, 28, 31, 40, 48, 55, 61, 67, 68, 76, 88, 91, 96, 97, 103,
    116, 124, 127, 133, 136, 139}, {0, 19, 23, 24, 30, 31, 36, 43, 60,
     66, 67, 71, 72, 79, 91, 96, 102, 108, 115, 119, 127, 132, 138,
    139}, {0, 19, 24, 25, 28, 31, 36, 48, 55, 61, 67, 72, 76, 84, 91,
    96, 97, 103, 120, 124, 127, 132, 133, 139}, {0, 19, 24, 25, 31,
    36, 44, 48, 55, 61, 67, 72, 84, 91, 92, 96, 97, 103, 120, 127,
    132, 133, 139, 140}, {0, 19, 24, 27, 30, 36, 39, 47, 60, 66, 67,
    72, 75, 87, 95, 96, 102, 108, 115, 123, 132, 135, 138, 143}, {0,
    19, 24, 30, 31, 36, 39, 43, 60, 66, 67, 72, 79, 87, 91, 96, 102,
    108, 115, 127, 132, 135, 138, 139}, {0, 19, 24, 30, 36, 39, 43,
    47, 60, 66, 67, 72, 87, 91, 95, 96, 102, 108, 115, 132, 135, 138,
    139, 143}, {0, 20, 21, 24, 27, 28, 33, 48, 57, 63, 68, 69, 72, 76,
     93, 96, 99, 105, 116, 120, 124, 129, 135, 141}, {0, 20, 21, 27,
    28, 33, 40, 48, 57, 63, 68, 69, 76, 88, 93, 96, 99, 105, 116, 124,
     129, 135, 136, 141}, {0, 20, 21, 27, 33, 40, 44, 48, 57, 63, 68,
    69, 88, 92, 93, 96, 99, 105, 116, 129, 135, 136, 140, 141}, {0,
    20, 23, 24, 28, 29, 35, 48, 59, 65, 68, 71, 72, 76, 95, 96, 101,
    107, 116, 120, 124, 131, 137, 143}, {0, 20, 23, 28, 29, 35, 40,
    48, 59, 65, 68, 71, 76, 88, 95, 96, 101, 107, 116, 124, 131, 136,
    137, 143}, {0, 20, 23, 29, 35, 40, 44, 48, 59, 65, 68, 71, 88, 92,
     95, 96, 101, 107, 116, 131, 136, 137, 140, 143}, {0, 21, 24, 25,
    30, 33, 36, 45, 60, 66, 69, 72, 73, 81, 93, 96, 102, 108, 117,
    121, 129, 132, 138, 141}, {0, 21, 24, 27, 28, 33, 36, 48, 57, 63,
    69, 72, 76, 84, 93, 96, 99, 105, 120, 124, 129, 132, 135,
    141}, {0, 21, 24, 27, 33, 36, 44, 48, 57, 63, 69, 72, 84, 92, 93,
    96, 99, 105, 120, 129, 132, 135, 140, 141}, {0, 21, 24, 29, 30,
    33, 36, 41, 60, 66, 69, 72, 77, 81, 89, 96, 102, 108, 117, 125,
    129, 132, 137, 138}, {0, 21, 24, 30, 33, 36, 41, 45, 60, 66, 69,
    72, 81, 89, 93, 96, 102, 108, 117, 129, 132, 137, 138, 141}, {0,
    21, 27, 28, 33, 36, 40, 48, 57, 63, 69, 76, 84, 88, 93, 96, 99,
    105, 124, 129, 132, 135, 136, 141}, {0, 23, 24, 27, 30, 35, 36,
    47, 60, 66, 71, 72, 75, 83, 95, 96, 102, 108, 119, 123, 131, 132,
    138, 143}, {0, 23, 24, 28, 29, 35, 36, 48, 59, 65, 71, 72, 76, 84,
     95, 96, 101, 107, 120, 124, 131, 132, 137, 143}, {0, 23, 24, 29,
    35, 36, 44, 48, 59, 65, 71, 72, 84, 92, 95, 96, 101, 107, 120,
    131, 132, 137, 140, 143}, {0, 23, 24, 30, 31, 35, 36, 43, 60, 66,
    71, 72, 79, 83, 91, 96, 102, 108, 119, 127, 131, 132, 138,
    139}, {0, 23, 24, 30, 35, 36, 43, 47, 60, 66, 71, 72, 83, 91, 95,
    96, 102, 108, 119, 131, 132, 138, 139, 143}, {0, 23, 28, 29, 35,
    36, 40, 48, 59, 65, 71, 76, 84, 88, 95, 96, 101, 107, 124, 131,
    132, 136, 137, 143}, {0, 24, 25, 29, 30, 33, 36, 37, 60, 66, 72,
    73, 77, 81, 85, 96, 102, 108, 121, 125, 129, 132, 133, 138}, {0,
    24, 25, 30, 33, 36, 37, 45, 60, 66, 72, 73, 81, 85, 93, 96, 102,
    108, 121, 129, 132, 133, 138, 141}, {0, 24, 27, 30, 31, 35, 36,
    39, 60, 66, 72, 75, 79, 83, 87, 96, 102, 108, 123, 127, 131, 132,
    135, 138}, {0, 24, 27, 30, 35, 36, 39, 47, 60, 66, 72, 75, 83, 87,
     95, 96, 102, 108, 123, 131, 132, 135, 138, 143}, {0, 24, 29, 30,
    33, 36, 37, 41, 60, 66, 72, 77, 81, 85, 89, 96, 102, 108, 125,
    129, 132, 133, 137, 138}, {0, 24, 30, 31, 35, 36, 39, 43, 60, 66,
    72, 79, 83, 87, 91, 96, 102, 108, 127, 131, 132, 135, 138,
    139}, {0, 24, 30, 33, 36, 37, 41, 45, 60, 66, 72, 81, 85, 89, 93,
    96, 102, 108, 129, 132, 133, 137, 138, 141}, {0, 24, 30, 35, 36,
    39, 43, 47, 60, 66, 72, 83, 87, 91, 95, 96, 102, 108, 131, 132,
    135, 138, 139, 143}};


There are 6 tiles for {3,4}:

T2 = {{0, 32, 58, 90, 112, 122}, {0, 46, 64, 110, 126, 128}, {0, 54,
    64, 80, 118, 134}, {0, 58, 74, 90, 112, 128}, {0, 62, 80, 94, 112,
     126}, {0, 94, 110, 112, 126, 128}};