Design generators for 2-level designs

The following table shows the design generators for 2-level factorial designs. The first line for each design gives the number of factors, the number of runs , the resolution of the design without blocking, and the design generators for the base design. Under the design generators, we display the block generators for blocked designs. 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. For example, 2(AB)3 indicates that the design has 2 blocks, the block generator is AB, and the resolution of the design is 3.

Factors Runs Resolution Design Generators
2 4 - Full

2(AB)3

3 4 III C=AB

No blocking

3 8 - Full

2(ABC)4 4(AB,AC)3

4 8 IV 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 III D=AB, E=AC

2(BC)3

5 16 V E=ABCD (E=ABC for 8 blocks)

2(AB)3 4(AB,AC)3 8(AB,AC,AD)3

5 16 V 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 III D=AB, E=AC, F=BC

2(BE)3

6 16 IV E=ABC, F=BCD

2(ACD)4 4(AE,ACD)3 8(AB,BC,BF)3

6 32 VI 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 III D=AB, E=AC, F=BC, G=ABC

no blocking

7 16 IV E=ABC, F=BCD, G=ACD

2(ABD)4 4(AB,AC)3 8(AB,AC,AD)3

7 32 IV F=ABCD, G=ABDE

2(CDE)4 4(CF,CDE)3 8(AB,AD,CG)3

7 64 VII 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 IV E=BCD, F=ACD, G=ABC, H=ABD

2(AB)3 4(AB,AC)3 8(AB,AC,AD)3

8 32 IV F=ABC, G=ABD, H=BCDE

2(ABE)4 4(EH,ABE)3 8(AB,AC,BD)3

8 64 V G=ABCD, H=ABEF

2(ACE)4 4(ACE,BDF)4 8(BC,FH,BDF)3 16(BC,DE,FH,BDF)3

8 128 VIII H=ABCDEFG

2(ABCD)5 4(ABCD,ABEF)5 8(ABCD,ABEF,BCEG)5 16(BF,DE,ABG,AEH)3 32(AC,BD,BF,DE,AEH)3

9 16 III

E=ABC, F=BCD, G=ACD, H=ABD, J =ABCD

2(AB)3 4(AB,AC)3

9 32 IV F=BCDE,G=ACDE,H=ABDE,J=ABCE

2(AEF)4 4(AB,CD)3 8(AB,AC,CD)3

9 64 IV 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 VI H=ACDFG, J=BCEFG

2(CDEJ)5 4(ABFJ,CDEJ)5 8(ACF,AHJ,BCJ)4 16(AE,CG,BCJ,BDE)3

10 16 III E=ABC, F=BCD, G=ACD, H=ABD, J =ABCD, K=AB

2(AC)3 4(AD,AG)3

10 32 IV F=BCDE,G=ACDE,H=ABDE,J=ABCE

2(AB)3 4(AB,BC)3 8(AB,AC,AH)3

10 64 IV 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 V 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 III

E=ABC, F=BCD, G=ACD, H=ABD, J=ABCD, K=AB, L=AC

2(AD)3 4(AE,AH)3

11 32 IV 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 IV 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 V H=ABCG, J=BCDE, K=ACDF

2(ADJ)4 4(ADJ,BFH)4 8(ADJ,AHL,BFH)4 16(BC,DF,GL,BFH)3

12 16 III 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 IV 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 IV 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 IV 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 III E=ABC, F=ABD, G=ACD, H=BCD, J=ABCD, K=AB, L=AC, M=AD, N=BC

2(AG)3

13 32 IV 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 IV 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 IV H=DEFG, J=BCEG, K=BCDFG, L=ABDEF, M=ACEF, N=ABC

2(ACF)4 4(BG,BJ)3 8(BG,BJ,AGM)3 16(BG,BJ,FM,AGM)3

14 16 III 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 IV 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 IV 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 IV 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 III 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 IV 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 IV 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 IV 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

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