//file for J2

 load simgps;
Loading "/applic/magma2.4/libs/simgps/simgps"
 g:=SimGroup("J2");
  re:=SimRecord("J2");
  ma:=re`Max;
//J2 of degree 100 

 g1:=ma[1];
 a1,a2,a3:=CosetAction(g,g1); 
 Degree(a2);
100
 pr:=[2,3,5,7,11];
 st:=Stabilizer(a2,1);
   orbs:=Orbits(st);"no. of orbs=",#orbs;
no. of orbs= 3
   lo:=[#orbs[i]: i in [1..#orbs]];lo;
[ 1, 63, 36 ]
 v:=Index(a2,st);"degree=",v;
degree= 100
 for j:=2 to #orbs do
 "orbs no",j,"of length",#orbs[j];
 edg:={1,Setseq(orbs[j])[1]}^a2;
 gr:=Graph<v|edg>;"no of edges=",#edg;
 "valence=",Valence(gr),"girth=",Girth(gr),
 "diameter=",Diameter(gr);
 #(AutomorphismGroup(gr));
   blox:=Setseq(orbs[j]^a2);
 des:=Design<1,v|blox>;des;
 #(AutomorphismGroup(des));
  for i:=1 to 5 do
  p:=pr[i];dc:=descode(v,blox,p);
 d1:=Dim(dc);d2:=Dim(Dual(dc));
 d3:=Dim(dc meet Dual(dc)); 
 "p=",p,"dim=",d1,"dimdual=",d2,"hull=",d3;
  end for;
   end for;
orbs no 2 of length 63
no of edges= 3150
valence= 63 girth= 3 diameter= 2
1209600
1-(100, 63, 63) Design with 100 blocks
1209600
p= 2 dim= 100 dimdual= 0 hull= 0
p= 3 dim= 36 dimdual= 64 hull= 0
p= 5 dim= 100 dimdual= 0 hull= 0
p= 7 dim= 63 dimdual= 37 hull= 0
p= 11 dim= 100 dimdual= 0 hull= 0
orbs no 3 of length 36
no of edges= 1800
valence= 36 girth= 3 diameter= 2
1209600
1-(100, 36, 36) Design with 100 blocks
1209600
p= 2 dim= 36 dimdual= 64 hull= 36
p= 3 dim= 63 dimdual= 37 hull= 0
p= 5 dim= 100 dimdual= 0 hull= 0
p= 7 dim= 100 dimdual= 0 hull= 0
p= 11 dim= 100 dimdual= 0 hull= 0
 
--------------------------------
//J2 of degree 280

> g2:=ma[2];
Permutation group a2 acting on a set of cardinality 280
Order = 604800 = 2^7 * 3^3 * 5^2 * 7
   orbs:=Orbits(st);"no. of orbs=",#orbs;
no. of orbs= 4
  lo:=[#orbs[i]: i in [1..#orbs]];lo;
[ 1, 135, 108, 36 ]
degree= 280

orbs no 2 of length 135
no of edges= 18900
valence= 135 girth= 3 diameter= 2
1209600
1-(280, 135, 135) Design with 280 blocks
1209600
p= 2 dim= 280 dimdual= 0 hull= 0
p= 3 dim= 216 dimdual= 64 hull= 0
p= 5 dim= 42 dimdual= 238 hull= 42
p= 7 dim= 280 dimdual= 0 hull= 0
p= 11 dim= 280 dimdual= 0 hull= 0
orbs no 3 of length 108
no of edges= 15120
valence= 108 girth= 3 diameter= 2
1209600
1-(280, 108, 108) Design with 280 blocks
1209600
p= 2 dim= 14 dimdual= 266 hull= 14
p= 3 dim= 216 dimdual= 64 hull= 0
p= 5 dim= 280 dimdual= 0 hull= 0
p= 7 dim= 280 dimdual= 0 hull= 0
p= 11 dim= 280 dimdual= 0 hull= 0
orbs no 4 of length 36
no of edges= 5040
valence= 36 girth= 3 diameter= 2
1209600
1-(280, 36, 36) Design with 280 blocks
1209600
p= 2 dim= 62 dimdual= 218 hull= 62
p= 3 dim= 279 dimdual= 1 hull= 0
p= 5 dim= 280 dimdual= 0 hull= 0
p= 7 dim= 280 dimdual= 0 hull= 0
p= 11 dim= 280 dimdual= 0 hull= 0
--------------------------------------
//J2 of degree 315

 g3:=ma[3];
[ 1, 80, 160, 10, 32, 32 ]
degree= 315

orbs no 2 of length 80
no of edges= 12600
valence= 80 girth= 3 diameter= 2
1209600
1-(315, 80, 80) Design with 315 blocks
1209600
p= 2 dim= 36 dimdual= 279 hull= 36
p= 3 dim= 315 dimdual= 0 hull= 0
p= 5 dim= 265 dimdual= 50 hull= 15
p= 7 dim= 315 dimdual= 0 hull= 0
p= 11 dim= 315 dimdual= 0 hull= 0
orbs no 3 of length 160
no of edges= 25200
valence= 160 girth= 3 diameter= 2
1209600
1-(315, 160, 160) Design with 315 blocks
1209600
p= 2 dim= 188 dimdual= 127 hull= 28
p= 3 dim= 279 dimdual= 36 hull= 0
p= 5 dim= 265 dimdual= 50 hull= 15
p= 7 dim= 155 dimdual= 160 hull= 36
p= 11 dim= 279 dimdual= 36 hull= 0
orbs no 4 of length 10
no of edges= 1575
valence= 10 girth= 3 diameter= 4
1209600
1-(315, 10, 10) Design with 315 blocks
1209600
p= 2 dim= 154 dimdual= 161 hull= 0
p= 3 dim= 225 dimdual= 90 hull= 0
p= 5 dim= 265 dimdual= 50 hull= 15
p= 7 dim= 315 dimdual= 0 hull= 0
p= 11 dim= 315 dimdual= 0 hull= 0
orbs no 5 of length 32
no of edges= 5040
valence= 32 girth= 3 diameter= 3
604800
1-(315, 32, 32) Design with 315 blocks
604800
p= 2 dim= 188 dimdual= 127 hull= 28
p= 3 dim= 315 dimdual= 0 hull= 0
p= 5 dim= 315 dimdual= 0 hull= 0
p= 7 dim= 315 dimdual= 0 hull= 0
p= 11 dim= 301 dimdual= 14 hull= 0
orbs no 6 of length 32
no of edges= 5040
valence= 32 girth= 3 diameter= 3
604800
1-(315, 32, 32) Design with 315 blocks
604800
p= 2 dim= 188 dimdual= 127 hull= 28
p= 3 dim= 315 dimdual= 0 hull= 0
p= 5 dim= 315 dimdual= 0 hull= 0
p= 7 dim= 315 dimdual= 0 hull= 0
p= 11 dim= 301 dimdual= 14 hull= 0
> lo;
[ 1, 80, 160, 10, 32, 32 ]

> des5:=Design<1,v|Setseq(orbs[5]^a2)>;
> des6:=Design<1,v|Setseq(orbs[6]^a2)>;
> a,b:=IsIsomorphic(des5,des6);
> a;
true
> b;
Mapping from: Dsgn: des5 to Dsgn: des6
> bl:=orbs[5] join orbs[6];
> des56:=Design<1,v|Setseq(bl^a2)>;
> des56;
1-(315, 64, 64) Design with 315 blocks
> #(AutomorphismGroup(des56));
1209600
----------------------------------------
//J2 of degree 525

 g4:=ma[4];
525
no. of orbs= 6
[ 1, 96, 192, 12, 192, 32 ]
degree= 525

orbs no 2 of length 96
no of edges= 25200
valence= 96 girth= 3 diameter= 2
1209600
1-(525, 96, 96) Design with 525 blocks
1209600
p= 2 dim= 98 dimdual= 427 hull= 62
p= 3 dim= 126 dimdual= 399 hull= 0
p= 5 dim= 525 dimdual= 0 hull= 0
p= 7 dim= 525 dimdual= 0 hull= 0
p= 11 dim= 525 dimdual= 0 hull= 0
orbs no 3 of length 192
no of edges= 50400
valence= 192 girth= 3 diameter= 2
1209600
1-(525, 192, 192) Design with 525 blocks
1209600
p= 2 dim= 112 dimdual= 413 hull= 112
p= 3 dim= 63 dimdual= 462 hull= 0
p= 5 dim= 525 dimdual= 0 hull= 0
p= 7 dim= 525 dimdual= 0 hull= 0
p= 11 dim= 525 dimdual= 0 hull= 0
orbs no 4 of length 12
no of edges= 3150
valence= 12 girth= 3 diameter= 4
1209600
1-(525, 12, 12) Design with 525 blocks
1209600
p= 2 dim= 364 dimdual= 161 hull= 0
p= 3 dim= 260 dimdual= 265 hull= 134
p= 5 dim= 365 dimdual= 160 hull= 90
p= 7 dim= 365 dimdual= 160 hull= 36
p= 11 dim= 365 dimdual= 160 hull= 0
orbs no 5 of length 192
no of edges= 50400
valence= 192 girth= 3 diameter= 2
1209600
1-(525, 192, 192) Design with 525 blocks
1209600
p= 2 dim= 112 dimdual= 413 hull= 112
p= 3 dim= 260 dimdual= 265 hull= 134
p= 5 dim= 365 dimdual= 160 hull= 90
p= 7 dim= 365 dimdual= 160 hull= 36
p= 11 dim= 365 dimdual= 160 hull= 0
orbs no 6 of length 32
no of edges= 8400
valence= 32 girth= 3 diameter= 4
1209600
1-(525, 32, 32) Design with 525 blocks
1209600
p= 2 dim= 160 dimdual= 365 hull= 0
p= 3 dim= 462 dimdual= 63 hull= 0
p= 5 dim= 525 dimdual= 0 hull= 0
p= 7 dim= 525 dimdual= 0 hull= 0
p= 11 dim= 525 dimdual= 0 hull= 0
> lo;
[ 1, 96, 192, 12, 192, 32 ]
> des3:=Design<1,v|Setseq(orbs[3]^a2)>;
> des5:=Design<1,v|Setseq(orbs[5]^a2)>;
> IsIsomorphic(des3,des5);
false
> //good
------------------------------------------
// J2 of degree 840

 g5:=ma[5];
 Degree(a2);
840
no. of orbs= 7
[ 1, 180, 240, 20, 15, 360, 24 ]
degree= 840

orbs no 2 of length 180
no of edges= 75600
valence= 180 girth= 3 diameter= 2
1209600
1-(840, 180, 180) Design with 840 blocks
1209600
p= 2 dim= 280 dimdual= 560 hull= 120
p= 3 dim= 216 dimdual= 624 hull= 0
p= 5 dim= 517 dimdual= 323 hull= 42
p= 7 dim= 602 dimdual= 238 hull= 0
p= 11 dim= 602 dimdual= 238 hull= 0
orbs no 3 of length 240
no of edges= 100800
valence= 240 girth= 3 diameter= 2
1209600
1-(840, 240, 240) Design with 840 blocks
1209600
p= 2 dim= 120 dimdual= 720 hull= 120
p= 3 dim= 378 dimdual= 462 hull= 90
p= 5 dim= 692 dimdual= 148 hull= 42
p= 7 dim= 714 dimdual= 126 hull= 0
p= 11 dim= 714 dimdual= 126 hull= 0
orbs no 4 of length 20
no of edges= 8400
valence= 20 girth= 3 diameter= 4
1209600
1-(840, 20, 20) Design with 840 blocks
1209600
p= 2 dim= 350 dimdual= 490 hull= 230
p= 3 dim= 714 dimdual= 126 hull= 90
p= 5 dim= 692 dimdual= 148 hull= 42
p= 7 dim= 714 dimdual= 126 hull= 0
p= 11 dim= 714 dimdual= 126 hull= 0
orbs no 5 of length 15
no of edges= 6300
valence= 15 girth= 3 diameter= 4
1209600
1-(840, 15, 15) Design with 840 blocks
1209600
p= 2 dim= 680 dimdual= 160 hull= 0
p= 3 dim= 504 dimdual= 336 hull= 0
p= 5 dim= 692 dimdual= 148 hull= 42
p= 7 dim= 840 dimdual= 0 hull= 0
p= 11 dim= 840 dimdual= 0 hull= 0
orbs no 6 of length 360
no of edges= 151200
valence= 360 girth= 3 diameter= 2
1209600
1-(840, 360, 360) Design with 840 blocks
1209600
p= 2 dim= 350 dimdual= 490 hull= 266
p= 3 dim= 216 dimdual= 624 hull= 0
p= 5 dim= 307 dimdual= 533 hull= 132
p= 7 dim= 455 dimdual= 385 hull= 0
p= 11 dim= 455 dimdual= 385 hull= 0
orbs no 7 of length 24
no of edges= 10080
valence= 24 girth= 3 diameter= 3
1209600
1-(840, 24, 24) Design with 840 blocks
1209600
p= 2 dim= 350 dimdual= 490 hull= 266
p= 3 dim= 350 dimdual= 490 hull= 134
p= 5 dim= 455 dimdual= 385 hull= 90
p= 7 dim= 455 dimdual= 385 hull= 0
p= 11 dim= 455 dimdual= 385 hull= 0
> lo;
[ 1, 180, 240, 20, 15, 360, 24 ]
> bl:=orbs[1] join orbs[7];
> blox:=Setseq(bl^a2);
> #blox;
840
> des17:=Design<1,v|blox>;
> des17;
1-(840, 25, 25) Design with 840 blocks
> AutomorphismGroup(des17);
Permutation group acting on a set of cardinality 840
Order = 1209600 = 2^8 * 3^3 * 5^2 * 7
-----------------------------------------
//J2 of degree 1008

 g6:=ma[6];
 Degree(a2);
1008
no. of orbs= 11
[ 1, 300, 12, 100, 60, 150, 150, 60, 100, 25, 50 ]
degree= 1008

orbs no 2 of length 300
1-(1008, 300, 300) Design with 1008 blocks
1209600
p= 2 dim= 628 dimdual= 380 hull= 152
p= 3 dim= 729 dimdual= 279 hull= 0
p= 5 dim= 560 dimdual= 448 hull= 85
p= 7 dim= 1008 dimdual= 0 hull= 0
p= 11 dim= 918 dimdual= 90 hull= 0
orbs no 3 of length 12
1-(1008, 12, 12) Design with 1008 blocks
1209600
p= 2 dim= 628 dimdual= 380 hull= 152
p= 3 dim= 729 dimdual= 279 hull= 0
p= 5 dim= 1008 dimdual= 0 hull= 0
p= 7 dim= 1008 dimdual= 0 hull= 0
p= 11 dim= 1008 dimdual= 0 hull= 0
orbs no 4 of length 100
1-(1008, 100, 100) Design with 1008 blocks
604800
p= 2 dim= 714 dimdual= 294 hull= 238
p= 3 dim= 882 dimdual= 126 hull= 90
p= 5 dim= 574 dimdual= 434 hull= 99
p= 7 dim= 882 dimdual= 126 hull= 0
p= 11 dim= 708 dimdual= 300 hull= 0
orbs no 5 of length 60
1-(1008, 60, 60) Design with 1008 blocks
604800
p= 2 dim= 714 dimdual= 294 hull= 238
p= 3 dim= 693 dimdual= 315 hull= 90
p= 5 dim= 678 dimdual= 330 hull= 99
p= 7 dim= 882 dimdual= 126 hull= 0
p= 11 dim= 792 dimdual= 216 hull= 0
orbs no 6 of length 150
1-(1008, 150, 150) Design with 1008 blocks
604800
p= 2 dim= 243 dimdual= 765 hull= 215
p= 3 dim= 441 dimdual= 567 hull= 225
p= 5 dim= 574 dimdual= 434 hull= 99
p= 7 dim= 719 dimdual= 289 hull= 89
p= 11 dim= 720 dimdual= 288 hull= 0
orbs no 7 of length 150
1-(1008, 150, 150) Design with 1008 blocks
604800
p= 2 dim= 243 dimdual= 765 hull= 215
p= 3 dim= 441 dimdual= 567 hull= 225
p= 5 dim= 574 dimdual= 434 hull= 99
p= 7 dim= 719 dimdual= 289 hull= 89
p= 11 dim= 720 dimdual= 288 hull= 0
orbs no 8 of length 60
1-(1008, 60, 60) Design with 1008 blocks
604800
p= 2 dim= 714 dimdual= 294 hull= 238
p= 3 dim= 693 dimdual= 315 hull= 90
p= 5 dim= 678 dimdual= 330 hull= 99
p= 7 dim= 882 dimdual= 126 hull= 0
p= 11 dim= 792 dimdual= 216 hull= 0
orbs no 9 of length 100
1-(1008, 100, 100) Design with 1008 blocks
604800
p= 2 dim= 714 dimdual= 294 hull= 238
p= 3 dim= 882 dimdual= 126 hull= 90
p= 5 dim= 574 dimdual= 434 hull= 99
p= 7 dim= 882 dimdual= 126 hull= 0
p= 11 dim= 708 dimdual= 300 hull= 0
orbs no 10 of length 25
1-(1008, 25, 25) Design with 1008 blocks
1209600
p= 2 dim= 1008 dimdual= 0 hull= 0
p= 3 dim= 1008 dimdual= 0 hull= 0
p= 5 dim= 560 dimdual= 448 hull= 85
p= 7 dim= 1008 dimdual= 0 hull= 0
p= 11 dim= 918 dimdual= 90 hull= 0
orbs no 11 of length 50
1-(1008, 50, 50) Design with 1008 blocks
1209600
p= 2 dim= 266 dimdual= 742 hull= 238
p= 3 dim= 630 dimdual= 378 hull= 225
p= 5 dim= 574 dimdual= 434 hull= 99
p= 7 dim= 630 dimdual= 378 hull= 0
p= 11 dim= 630 dimdual= 378 hull= 0
> lo;
[ 1, 300, 12, 100, 60, 150, 150, 60, 100, 25, 50 ]
> bl:=orbs[4] join orbs[9];
> des49:=Design<1,v|Setseq(bl^a2)>;
> des49;
1-(1008, 200, 200) Design with 1008 blocks
> AutomorphismGroup(des49);
Permutation group acting on a set of cardinality 1008
Order = 1209600 = 2^8 * 3^3 * 5^2 * 7
> bl:=orbs[5] join orbs[8];
> des58:=Design<1,v|Setseq(bl^a2)>;
>  AutomorphismGroup(des58);
Permutation group acting on a set of cardinality 1008
Order = 1209600 = 2^8 * 3^3 * 5^2 * 7
> des5:=Design<1,v|Setseq(orbs[5]^a2)>;
> des8:=Design<1,v|Setseq(orbs[8]^a2)>;
> IsIsomorphic(des5,des8);
true Mapping from: Dsgn: des5 to Dsgn: des8
> bl:=orbs[6] join orbs[7];
> des67:=Design<1,v|Setseq(bl^a2)>;
> des67;
1-(1008, 300, 300) Design with 1008 blocks
> AutomorphismGroup(des67);
Permutation group acting on a set of cardinality 1008
Order = 1209600 = 2^8 * 3^3 * 5^2 * 7
--------------------------------------------------
//J2 of degree 1800

 g7:=ma[7];
Permutation group a2 acting on a set of cardinality 1800
Order = 604800 = 2^7 * 3^3 * 5^2 * 7
no. of orbs= 18
[ 1, 14, 14, 42, 168, 168, 168, 84, 84, 168, 168, 336, 28, 42, 168,
84, 42, 21 ]
degree= 1800

orbs no 2 of length 14
1-(1800, 14, 14) Design with 1800 blocks
604800
p= 2 dim= 1134 dimdual= 666 hull= 62
p= 3 dim= 1611 dimdual= 189 hull= 36
p= 5 dim= 1800 dimdual= 0 hull= 0
p= 7 dim= 1337 dimdual= 463 hull= 0
p= 11 dim= 1800 dimdual= 0 hull= 0
orbs no 3 of length 14
1-(1800, 14, 14) Design with 1800 blocks
604800
p= 2 dim= 1134 dimdual= 666 hull= 62
p= 3 dim= 1611 dimdual= 189 hull= 36
p= 5 dim= 1800 dimdual= 0 hull= 0
p= 7 dim= 1337 dimdual= 463 hull= 0
p= 11 dim= 1800 dimdual= 0 hull= 0
orbs no 4 of length 42
1-(1800, 42, 42) Design with 1800 blocks
1209600
p= 2 dim= 700 dimdual= 1100 hull= 364
p= 3 dim= 1050 dimdual= 750 hull= 489
p= 5 dim= 1625 dimdual= 175 hull= 0
p= 7 dim= 1624 dimdual= 176 hull= 0
p= 11 dim= 1589 dimdual= 211 hull= 0
orbs no 5 of length 168
1-(1800, 168, 168) Design with 1800 blocks
1209600
p= 2 dim= 568 dimdual= 1232 hull= 120
p= 3 dim= 1401 dimdual= 399 hull= 336
p= 5 dim= 1625 dimdual= 175 hull= 0
p= 7 dim= 1624 dimdual= 176 hull= 0
p= 11 dim= 1625 dimdual= 175 hull= 0
orbs no 6 of length 168
1-(1800, 168, 168) Design with 1800 blocks
1209600
p= 2 dim= 336 dimdual= 1464 hull= 336
p= 3 dim= 1401 dimdual= 399 hull= 336
p= 5 dim= 1625 dimdual= 175 hull= 0
p= 7 dim= 1624 dimdual= 176 hull= 0
p= 11 dim= 1625 dimdual= 175 hull= 0
orbs no 7 of length 168
1-(1800, 168, 168) Design with 1800 blocks
1209600
p= 2 dim= 448 dimdual= 1352 hull= 0
p= 3 dim= 1401 dimdual= 399 hull= 336
p= 5 dim= 1625 dimdual= 175 hull= 0
p= 7 dim= 1624 dimdual= 176 hull= 0
p= 11 dim= 1625 dimdual= 175 hull= 0
orbs no 8 of length 84
1-(1800, 84, 84) Design with 1800 blocks
604800
p= 2 dim= 734 dimdual= 1066 hull= 398
p= 3 dim= 1050 dimdual= 750 hull= 489
p= 5 dim= 1199 dimdual= 601 hull= 336
p= 7 dim= 1261 dimdual= 539 hull= 36
p= 11 dim= 1262 dimdual= 538 hull= 0
orbs no 9 of length 84
1-(1800, 84, 84) Design with 1800 blocks
1209600
p= 2 dim= 734 dimdual= 1066 hull= 398
p= 3 dim= 1176 dimdual= 624 hull= 399
p= 5 dim= 1800 dimdual= 0 hull= 0
p= 7 dim= 1736 dimdual= 64 hull= 63
p= 11 dim= 1800 dimdual= 0 hull= 0
orbs no 10 of length 168
1-(1800, 168, 168) Design with 1800 blocks
604800
p= 2 dim= 336 dimdual= 1464 hull= 336
p= 3 dim= 939 dimdual= 861 hull= 372
p= 5 dim= 1800 dimdual= 0 hull= 0
p= 7 dim= 1799 dimdual= 1 hull= 0
p= 11 dim= 1800 dimdual= 0 hull= 0
orbs no 11 of length 168
1-(1800, 168, 168) Design with 1800 blocks
604800
p= 2 dim= 336 dimdual= 1464 hull= 336
p= 3 dim= 939 dimdual= 861 hull= 372
p= 5 dim= 1800 dimdual= 0 hull= 0
p= 7 dim= 1799 dimdual= 1 hull= 0
p= 11 dim= 1800 dimdual= 0 hull= 0
orbs no 12 of length 336
1-(1800, 336, 336) Design with 1800 blocks
1209600
p= 2 dim= 120 dimdual= 1680 hull= 120
p= 3 dim= 1275 dimdual= 525 hull= 372
p= 5 dim= 1450 dimdual= 350 hull= 315
p= 7 dim= 1673 dimdual= 127 hull= 0
p= 11 dim= 1674 dimdual= 126 hull= 0
orbs no 13 of length 28
1-(1800, 28, 28) Design with 1800 blocks
1209600
p= 2 dim= 798 dimdual= 1002 hull= 350
p= 3 dim= 1512 dimdual= 288 hull= 63
p= 5 dim= 1800 dimdual= 0 hull= 0
p= 7 dim= 1799 dimdual= 1 hull= 0
p= 11 dim= 1800 dimdual= 0 hull= 0
orbs no 14 of length 42
1-(1800, 42, 42) Design with 1800 blocks
604800
p= 2 dim= 1072 dimdual= 728 hull= 0
p= 3 dim= 1401 dimdual= 399 hull= 336
p= 5 dim= 1640 dimdual= 160 hull= 90
p= 7 dim= 1639 dimdual= 161 hull= 36
p= 11 dim= 1640 dimdual= 160 hull= 0
orbs no 15 of length 168
1-(1800, 168, 168) Design with 1800 blocks
1209600
p= 2 dim= 336 dimdual= 1464 hull= 336
p= 3 dim= 1401 dimdual= 399 hull= 336
p= 5 dim= 1625 dimdual= 175 hull= 0
p= 7 dim= 1624 dimdual= 176 hull= 0
p= 11 dim= 1625 dimdual= 175 hull= 0
orbs no 16 of length 84
1-(1800, 84, 84) Design with 1800 blocks
604800
p= 2 dim= 734 dimdual= 1066 hull= 398
p= 3 dim= 1050 dimdual= 750 hull= 489
p= 5 dim= 1199 dimdual= 601 hull= 336
p= 7 dim= 1261 dimdual= 539 hull= 36
p= 11 dim= 1262 dimdual= 538 hull= 0
orbs no 17 of length 42
1-(1800, 42, 42) Design with 1800 blocks
604800
p= 2 dim= 1072 dimdual= 728 hull= 0
p= 3 dim= 1401 dimdual= 399 hull= 336
p= 5 dim= 1640 dimdual= 160 hull= 90
p= 7 dim= 1639 dimdual= 161 hull= 36
p= 11 dim= 1640 dimdual= 160 hull= 0
orbs no 18 of length 21
1-(1800, 21, 21) Design with 1800 blocks
1209600
p= 2 dim= 1352 dimdual= 448 hull= 0
p= 3 dim= 939 dimdual= 861 hull= 426
p= 5 dim= 1800 dimdual= 0 hull= 0
p= 7 dim= 1673 dimdual= 127 hull= 0
p= 11 dim= 1737 dimdual= 63 hull= 0
------------------------------------

//J2 of degree 2016

Loading "/usr/local/magma2.3/LIBS/simgps/simgps"
Permutation group a2 acting on a set of cardinality 2016
Order = 604800 = 2^7 * 3^3 * 5^2 * 7
no. of orbs= 18

[ 1, 50, 150, 75, 75, 300, 150, 50, 75, 150, 150, 15, 150, 300, 150,
25, 75, 75 ]
degree= 2016

orbs no 2 of length 50
1-(2016, 50, 50) Design with 2016 blocks
604800
p= 2 dim= 797 dimdual= 1219 hull= 363
p= 3 dim= 1665 dimdual= 351 hull= 225
p= 5 dim= 1575 dimdual= 441 hull= 315
p= 7 dim= 1601 dimdual= 415 hull= 89
p= 11 dim= 1728 dimdual= 288 hull= 0
orbs no 3 of length 150
1-(2016, 150, 150) Design with 2016 blocks
604800
p= 2 dim= 796 dimdual= 1220 hull= 362
p= 3 dim= 1617 dimdual= 399 hull= 336
p= 5 dim= 1855 dimdual= 161 hull= 90
p= 7 dim= 1419 dimdual= 597 hull= 124
p= 11 dim= 1856 dimdual= 160 hull= 0
orbs no 4 of length 75
1-(2016, 75, 75) Design with 2016 blocks
604800
p= 2 dim= 1568 dimdual= 448 hull= 0
p= 3 dim= 1491 dimdual= 525 hull= 426
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 2016 dimdual= 0 hull= 0
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 5 of length 75
1-(2016, 75, 75) Design with 2016 blocks
1209600
p= 2 dim= 1568 dimdual= 448 hull= 0
p= 3 dim= 1281 dimdual= 735 hull= 336
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 1764 dimdual= 252 hull= 0
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 6 of length 300
1-(2016, 300, 300) Design with 2016 blocks
604800
p= 2 dim= 182 dimdual= 1834 hull= 182
p= 3 dim= 1617 dimdual= 399 hull= 336
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 1391 dimdual= 625 hull= 89
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 7 of length 150
1-(2016, 150, 150) Design with 2016 blocks
1209600
p= 2 dim= 546 dimdual= 1470 hull= 98
p= 3 dim= 827 dimdual= 1189 hull= 314
p= 5 dim= 1700 dimdual= 316 hull= 0
p= 7 dim= 2016 dimdual= 0 hull= 0
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 8 of length 50
1-(2016, 50, 50) Design with 2016 blocks
604800
p= 2 dim= 797 dimdual= 1219 hull= 363
p= 3 dim= 1665 dimdual= 351 hull= 225
p= 5 dim= 1575 dimdual= 441 hull= 315
p= 7 dim= 1601 dimdual= 415 hull= 89
p= 11 dim= 1728 dimdual= 288 hull= 0
orbs no 9 of length 75
1-(2016, 75, 75) Design with 2016 blocks
604800
p= 2 dim= 1568 dimdual= 448 hull= 0
p= 3 dim= 1617 dimdual= 399 hull= 336
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 2016 dimdual= 0 hull= 0
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 10 of length 150
1-(2016, 150, 150) Design with 2016 blocks
1209600
p= 2 dim= 448 dimdual= 1568 hull= 0
p= 3 dim= 1329 dimdual= 687 hull= 561
p= 5 dim= 1338 dimdual= 678 hull= 147
p= 7 dim= 2016 dimdual= 0 hull= 0
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 11 of length 150
1-(2016, 150, 150) Design with 2016 blocks
604800
p= 2 dim= 797 dimdual= 1219 hull= 363
p= 3 dim= 993 dimdual= 1023 hull= 561
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 2016 dimdual= 0 hull= 0
p= 11 dim= 1926 dimdual= 90 hull= 0
orbs no 12 of length 15
1-(2016, 15, 15) Design with 2016 blocks
1209600
p= 2 dim= 1568 dimdual= 448 hull= 0
p= 3 dim= 953 dimdual= 1063 hull= 224
p= 5 dim= 2015 dimdual= 1 hull= 0
p= 7 dim= 1890 dimdual= 126 hull= 0
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 13 of length 150
1-(2016, 150, 150) Design with 2016 blocks
604800
p= 2 dim= 796 dimdual= 1220 hull= 362
p= 3 dim= 1617 dimdual= 399 hull= 336
p= 5 dim= 1855 dimdual= 161 hull= 90
p= 7 dim= 1419 dimdual= 597 hull= 124
p= 11 dim= 1856 dimdual= 160 hull= 0
orbs no 14 of length 300
1-(2016, 300, 300) Design with 2016 blocks
604800
p= 2 dim= 182 dimdual= 1834 hull= 182
p= 3 dim= 1617 dimdual= 399 hull= 336
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 1391 dimdual= 625 hull= 89
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 15 of length 150
1-(2016, 150, 150) Design with 2016 blocks
604800
p= 2 dim= 797 dimdual= 1219 hull= 363
p= 3 dim= 993 dimdual= 1023 hull= 561
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 2016 dimdual= 0 hull= 0
p= 11 dim= 1926 dimdual= 90 hull= 0
orbs no 16 of length 25
1-(2016, 25, 25) Design with 2016 blocks
1209600
p= 2 dim= 2016 dimdual= 0 hull= 0
p= 3 dim= 2016 dimdual= 0 hull= 0
p= 5 dim= 1400 dimdual= 616 hull= 315
p= 7 dim= 1890 dimdual= 126 hull= 0
p= 11 dim= 1926 dimdual= 90 hull= 0
orbs no 17 of length 75
1-(2016, 75, 75) Design with 2016 blocks
604800
p= 2 dim= 1568 dimdual= 448 hull= 0
p= 3 dim= 1491 dimdual= 525 hull= 426
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 2016 dimdual= 0 hull= 0
p= 11 dim= 2016 dimdual= 0 hull= 0
orbs no 18 of length 75
1-(2016, 75, 75) Design with 2016 blocks
604800
p= 2 dim= 1568 dimdual= 448 hull= 0
p= 3 dim= 1617 dimdual= 399 hull= 336
p= 5 dim= 1925 dimdual= 91 hull= 0
p= 7 dim= 2016 dimdual= 0 hull= 0
p= 11 dim= 2016 dimdual= 0 hull= 0