star_to_spread function

Converts a star to its corresponding spread

A function that converts a balanced covering star St(n, mu, t, t_0) of PG(n-1,2) to its corresponding balanced ((t-t_0)-1)-spread of PG((n-t_0)-1,2).

star_to_spread(star)

Arguments

• star: A balanced covering star of PG(n-1,2) stored as a three dimensional binary array (see Details and Examples of checkSpreadEquivalence).

Details

Finds a balanced ((t-t_0)-1)-spread of PG((n-t_0)-1,2) embedded in PG(n-1,2) as conformable with the geometry of a balanced covering star St(n, mu, t, t_0) of PG(n-1,2). The star should be formatted as a 3-dimensional array with star[i,j,k] indicating whether or not the ith basic factor is present in the jth effect of the kth flat of star. See Spencer et al. (2019) for details.

Returns

A balanced ((t-t_0)-1)-spread of PG((n-t_0)-1,2)

References

Spencer, N.A., Ranjan, P., and Mendivil, F., (2019), "Isomorphism Check for $2^n$ Factorial Designs with Randomization Restrictions", Journal of Statistical Theory and Practice, 13(60),1-24 [https://doi.org/10.1007/s42519-019-0064-5]

See Also

is.spread for checking if the input is a balanced spread.

checkSpreadIsomorphism for checking the isomorphism of balanced spreads.

checkStarIsomorphism for checking the isomorphism of balanced covering stars.

Author(s)

Neil Spencer, Pritam Ranjan, Franklin Mendivil

Examples

## Example 1: checking whether "starn8t5a" is a proper star
data(starn8t5a)
star_to_spread(starn8t5a)


## Example 2: checking whether "starn5t3a" is a proper star
data(starn5t3a)
star_to_spread(starn5t3a)