Fries and Hunter · 1980

Minimum Aberration 2^(k-p) Designs

Factorial gives the paper's answers. Where they differ, this page says why: some are misprints in the paper.

Examples

Each example, and how closely Factorial gives its answers.

Misprints found in the paper, by page. Each shows what the paper prints and what its own data give.

Maximum resolution: 2^(12-5), 128 runsp. 605
Book VData 4
No 2^(12-5) reaches resolution V: an exhaustive search over every set of five generators (the base factors being interchangeable) finds none, and the binary [12, 5] codes have minimum distance at most 4. R_max is 4, which the design checked here reaches. The printed 5 is the paper's bound (3), which no design attains here, so the row should carry the asterisk
Maximum resolution: 2^(13-5), 256 runsp. 605
Book IVData 5
A 2^(13-5) of resolution V exists (these generators; none reaches VI), so R_max is 5. The printed 4 also contradicts the table's own row for 2^(14-6), R_max = 5 in the same 256 runs: removing a factor from that design leaves a 2^(13-5) of at least resolution V
Maximum resolution: 2^(13-3), 1024 runsp. 605
Book VIData 7
A 2^(13-3) of resolution VII exists (these generators), so R_max is 7. The paper's own equation (1) gives 7 here (13 = 1 x 7 + 6, so 4 x 1 + [6/2]), where the table prints 6 for bound (1) and bound (3) alike
Maximum resolution: 2^(14-5), 512 runsp. 605
Book VData 6
A 2^(14-5) of resolution VI exists (these generators), so R_max is 6 and equals the bound (3) printed beside it; the asterisk, saying the bound is not attained, does not hold
Maximum resolution: 2^(14-4), 1024 runsp. 605
Book VIData 7
A 2^(14-4) of resolution VII exists (these generators), so R_max is 7 and equals the bound (3) printed beside it; the asterisk, saying the bound is not attained, does not hold

Show the rest

Maximum resolution: 2^(14-3), 2048 runsp. 605
Book VIIData 8
A 2^(14-3) of resolution VIII exists: two factors in each of the seven cells of three generators, every word of length 8. R_max is 8, as the paper's own equation (1) gives (14 = 2 x 7, so 4 x 2), where the table prints 7 for bound (1), bound (3) and R_max alike

Answers the paper prints that Factorial cannot compute yet, by what it lacks.

A step of the paper's algorithm, which the library does not run; designs (b) and (c) of Table 1 have these patterns (checked above)p. 604
A step of the paper's algorithm: the numbers of letters in the cells of the generators, which the library does not computep. 604