Generators for 2-Level Designsmain topic
Generators for 2-Level DesignsThe first line for each design gives the number of factors, the number of runs, the resolution (R) of the design without blocking, and the design generators. On the following lines, there is one entry for each number of blocks. The number before the parentheses is the number of blocks, in the parentheses are the block generators, and the number after the parentheses is the resolution of the blocked design.
|
factor |
runs |
R |
Design Generators |
|
2 |
4 |
- |
Full |
|
|
|
|
2(AB)3 |
|
|
|
|
|
|
3 |
4 |
3 |
C=AB |
|
|
|
|
no blocking |
|
3 |
8 |
- |
Full |
|
|
|
|
2(ABC)4 4(AB,AC)3 |
|
|
|
|
|
|
4 |
8 |
4 |
D=ABC |
|
|
|
|
2(AB)3 4(AB,AC)3 |
|
4 |
16 |
- |
Full |
|
|
|
|
2(ABCD)5 4(BC,ABD)3 8(AB,BC,CD)3 |
|
|
|
|
|
|
5 |
8 |
3 |
D=AB,E=AC |
|
|
|
|
2(BC)3 |
|
5 |
16 |
5 |
E=ABCD (E=ABC for 8 blocks) |
|
|
|
|
2(AB)3 4(AB,AC)3 8(AB,AC,AD)3 |
|
5 |
32 |
- |
Full |
|
|
|
|
2(ABCDE)6 4(ABC,CDE)4 8(AC,BD,ADE)3 16(AB,AC,CD,DE)3 |
|
|
|
|
|
|
6 |
8 |
3 |
D=AB,E=AC,F=BC |
|
|
|
|
2(BE)3 |
|
6 |
16 |
4 |
E=ABC,F=BCD |
|
|
|
|
2(ACD)4 4(AE,ACD)3 8(AB,BC,BF)3 |
|
6 |
32 |
6 |
F=ABCDE |
|
|
|
|
2(ABF)4 4(BC,ABF)3 8(AD,BC,ABF)3 16(AB,BC,CD,DE)3 |
|
6 |
64 |
- |
Full |
|
|
|
|
2(ABCDEF)7 4(ABCF,ABDE)5 8(ACE,ADF,BCF)4 |
|
|
|
|
16(AD,BE,CE,ABF)3 32(AB,BC,CD,DE,EF)3 |
|
7 |
8 |
3 |
D=AB,E=AC,F=BC,G=ABC |
|
|
|
|
no blocking |
|
7 |
16 |
4 |
E=ABC,F=BCD,G=ACD |
|
|
|
|
2(ABD)4 4(AB,AC)3 8(AB,AC,AD)3 |
|
7 |
32 |
4 |
F=ABCD,G=ABDE |
|
|
|
|
2(CDE)4 4(CF,CDE)3 8(AB,AD,CG)3 |
|
7 |
64 |
7 |
G=ABCDEF |
|
|
|
|
2(CDE)4 4(ACF,CDE)4 8(ACF,ADG,CDE)4 16(AB,AC,EF,EG)3 |
|
7 |
128 |
- |
Full |
|
|
|
|
2(ABCDEFG)8 4(ABDE,ABCFG)5 8(ABC,AFG,DEF)4 16(ABE,ADG,CDE,EFG)4 32(AC,BD,CE,DF,ABG)3 64(AB,BC,CD,DE,EF,FG)3 |
|
|
|
|
|
|
8 |
16 |
4 |
E=BCD,F=ACD,G=ABC,H=ABD |
|
|
|
|
2(AB)3 4(AB,AC)3 8(AB,AC,AD)3 |
|
8 |
32 |
4 |
F=ABC,G=ABD,H=BCDE |
|
|
|
|
2(ABE)4 4(EH,ABE)3 8(AB,AC,BD)3 |
|
8 |
64 |
5 |
G=ABCD,H=ABEF |
|
|
|
|
2(ACE)4 4(ACE,BDF)4 8(BC,FH,BDF)3 16(BC,DE,FH,BDF)3 |
|
8 |
128 |
8 |
H=ABCDEFG |
|
|
|
|
2(ABCD)5 4(ABCD,ABEF)5 8(ABCD,ABEF,BCEG)5 |
|
|
|
|
|
|
9 |
16 |
3 |
E=ABC,F=BCD,G=ACD,H=ABD,J=ABCD |
|
|
|
|
2(AB)3 4(AB,AC)3 |
|
9 |
32 |
4 |
F=BCDE,G=ACDE,H=ABDE,J=ABCE |
|
|
|
|
2(AEF)4 4(AB,CD)3 8(AB,AC,CD)3 |
|
9 |
64 |
4 |
G=ABCD,H=ACEF,J=CDEF |
|
|
|
|
2(BCE)4 4(ABF,ACJ)4 8(AD,AH,BDE)3 16(AC,AD,AJ,BF)3 |
|
9 |
128 |
6 |
H=ACDFG,J=BCEFG |
|
|
|
|
2(CDEJ)5 4(ABFJ,CDEJ)5 8(ACF,AHJ,BCJ)4 16(AE,CG,BCJ,BDE)3 |
|
|
|
|
|
|
10 |
16 |
3 |
E=ABC,F=BCD,G=ACD,H=ABD,J=ABCD,K=AB |
|
|
|
|
2(AC)3 4(AD,AG)3 |
|
10 |
32 |
4 |
F=ABCD,G=ABCE,H=ABDE,J=ACDE,K=BCDE |
|
|
|
|
2(AB)3 4(AB,BC)3 8(AB,AC,AH)3 |
|
10 |
64 |
4 |
G=BCDF,H=ACDF,J=ABDE,K=ABCE |
|
|
|
|
2(AGJ)4 4(CD,AGJ)3 8(AG,CJ,CK)3 16(AC,AG,CJ,CK)3 |
|
10 |
128 |
5 |
H=ABCG,J=BCDE,K=ACDF |
|
|
|
|
2(ADG)4 4(ADG,BDF)4 8(AEH,AGK,CDH)4 16(BH,EG,JK,ADG)3 |
|
|
|
|
|
|
11 |
16 |
3 |
E=ABC,F=BCD,G=ACD,H=ABD,J=ABCD,K=AB,L=AC |
|
|
|
|
2(AD)3 4(AE,AH)3 |
|
11 |
32 |
4 |
F=ABC,G=BCD,H=CDE,J=ACD,K=ADE,L=BDE |
|
|
|
|
2(ABD)4 4(AK,ABD)3 8(AB,AC,AD)3 |
|
11 |
64 |
4 |
G=CDE,H=ABCD,J=ABF,K=BDEF,L=ADEF |
|
|
|
|
2(AHJ)4 4(FL,AHJ)3 8(CD,CE,DL)3 16(AB,AC,AE,AF)3 |
|
11 |
128 |
5 |
H=ABCG,J=BCDE,K=ACDF,L=ABCDEFG |
|
|
|
|
2(ADJ)4 4(ADJ,BFH)4 8(ADJ,AHL,BFH)4 16(BC,DF,GL,BFH)3 |
|
|
|
|
|
|
12 |
16 |
3 |
E=ABC,F=ABD,G=ACD,H=BCD,J=ABCD,K=AB,L=AC,M=AD |
|
|
|
|
2(AG)3 4(AF,AG)3 |
|
12 |
32 |
4 |
F=ACE,G=ACD,H=ABD,J=ABE,K=CDE,L=ABCDE,M=ADE |
|
|
|
|
2(ABC)4 4(DG,DH)3 8(AB,AC,AD)3 |
|
12 |
64 |
4 |
G=DEF,H=ABC,J=BCDE,K=BCDF,L=ABEF,M=ACEF |
|
|
|
|
2(ABM)4 4(AB,AC)3 8(AB,AC,BM)3 16(AB,AD,BE,BM)3 |
|
12 |
128 |
4 |
H=ACDG,J=ABCD,K=BCFG,L=ABDEFG,M=CDEF |
|
|
|
|
2(ACF)4 4(BG,BJ)3 8(BG,BJ,AGM)3 16(BG,BJ,FM,AGM)3 |
|
|
|
|
|
|
13 |
16 |
3 |
E=ABC,F=ABD,G=ACD,H=BCD,J=ABCD,K=AB,L=AC,M=AD,N=BC |
|
|
|
|
2(AG)3 |
|
13 |
32 |
4 |
F=ACE,G=BCE,H=ABC,J=CDE,K=ABCDE,L=ABE,M=ACD,N=ADE |
|
|
|
|
2(ABD)4 4(CG,GH)3 8(AB,AC,AD)3 |
|
13 |
64 |
4 |
G=ABC,H=DEF,J=BCDF,K=BCDE,L=ABEF,M=ACEF,N=BCEF |
|
|
|
|
2(AB)3 4(AB,AC)3 8(AB,AC,AN)3 16(AB,AD,BE,BM)3 |
|
13 |
128 |
4 |
H=DEFG,J=BCEG,K=BCDFG,L=ABDEF,M=ACEF,N=ABC |
|
|
|
|
2(ADE)4 4(AB,AC)3 8(AB,AC,AGK)3 16(AB,AC,ABM,AGK)3 |
|
|
|
|
|
|
14 |
16 |
3 |
E=ABC,F=ABD,G=ACD,H=BCD,J=ABCD,K=AB,L=AC,M=AD,N=BC,O=BD |
|
|
|
|
2(AG)3 |
|
14 |
32 |
4 |
F=ABC,G=ABD,H=ABE,J=ACD,K=ACE,L=ADE,M=BCD,N=BCE, O=BDE |
|
|
|
|
2(ACL)4 4(AB,ACL)3 8(AC,AL,AO)3 |
|
14 |
64 |
4 |
G=BEF,H=BCF,J=DEF,K=CEF,L=BCE,M=CDF,N=ACDE,O=BCDEF |
|
|
|
|
2(ABC)4 4(BC,BE)3 8(BC,BE,BG)3 16(AB,BC,BE,BG)3 |
|
14 |
128 |
4 |
H=EFG,J=BCFG,K=BCEG,L=ABEF,M=ACEF,N=BCDEF,O=ABC |
|
|
|
|
2(ADE)4 4(AB,AC)3 8(AB,AC,BM)3 16(AB,AC,BM,DG)3 |
|
|
|
|
|
|
15 |
16 |
3 |
E=ABC,F=ABD,G=ACD,H=BCD,J=ABCD,K=AB,L=AC,M=AD,N=BC,O=BD,P=CD |
|
|
|
|
no blocking |
|
15 |
32 |
4 |
F=ABC,G=ABD,H=ABE,J=ACD,K=ACE,L=ADE,M=BCD,N=BCE,O=BDE, P=CDE |
|
|
|
|
2(ABP)4 4(AB,BP)3 8(AB,AD,AK)3 |
|
15 |
64 |
4 |
G=ABC,H=ABD,J=ABE,K=ABF,L=ACD,M=ACE,N=ACF,O=ADE,P=ADF |
|
|
|
|
2(ABL)4 4(AM,ABL)3 8(AB,AC,AD)3 16(AB,AC,AD,AE)3 |
|
15 |
128 |
4 |
H=ABFG,J=ACDEF,K=BEF,L=ABCEG,M=CDFG,N=ACDEG,O=EFG, |
|
|
|
|
P=ABDEFG |
|
|
|
|
2(ADE)4 4(EG,GP)3 8(EG,GP,OP)3 16(BO,EG,GP,OP)3 |