NEWS

October 4 2026, version 0.24-3 - made the package description more informative - modified handling of NULL seeds: these are no longer made reproducible - added missing sections (@returns) - handled in examples: removed a few unneeded ones, changed slow but not extremely slow ones to , kept three in place for extremely slow code that should only be intentionally run by a user in an interactive session, and restricted automatically runnable very slow examples to being conditionally run if an option “run_heavy_examples” is set to TRUE (by @examplesIf) - changed the maximum number of parallel threads in examples to 2 - removed some print commands, replaced others with message - made a few minor edits

September 22 2026, version 0.24-2 - added missing usage entries for some N_- and k_-functions - shortened example times for powerCA and MTVTRouxtype

September 21 2026, version 0.24-1 - added version requirement for package caverify (because of logic applied for flexible values and applicability for mixed level CAs) - updated version number

September 05 2026, still version 0.24 - bug fix to function DHHF2CA (corrected the handling of constant rows, especially where a constant row needs to be added; this fixes a bug in powerCA, where the result of powerCA(3,1584,2) did not cover all 1,1,1 triples; found by Christopher Smolen) - added tests for DHHF2CA, and modified tests for powerCA - bug fix to function cyclotomyCA, by changing the type of three rows in CYCLOTOMYcat from the erroneous 3a (driven by a mistake in the Colbourn tables) to 4a (proven conclusively for the smallest case and by sampling only for the larger cases); this bug was also found by Christopher Smolen, who also did an extensive sampling check on the two larger cases - added an example for the main user function cyclotomyCA

August 2026, version 0.24 - moved external data to .Rbuildignore so that the R package is small enough - reduced example run time - imported package caverify in order to make use of the fast coverage checks of function ca_verify - made a few formal fixes for CRAN, like authors@R

February 24 2026, still version 0.23 - changed the acronym for “sequential covering array” to SeqCA instead of SCA in order to avoid confusion with the special structure CA that is abbreviated as SCA - added function SeqCA_Levenshtein for optimal strength t SeqCAs with t+1 columns - improved the perturbation in simulated annealing for the optimize_SCA function

February 21 2026, version 0.23 - added functionality for SCAs

November 21 2025, version 0.22 - added arrays from Walker and Colbourn 2009 for scphfCA - added classical (poor) augmentation constructions (CK_constrD and CKRS_augment), not included in function Ns - added the L81.3.5 to miscCAcat

October 11 2025, version 0.21 - improved the implementation of fusion in bestN, so that the speed of bestN is again in its prior range - added function add1 - added a reference for crossCAs

September 27 2025, version 0.20 - improved N_CS_LCDST to return the minimum and not the first entry, because a later entry is occasionally better - improved MCA2 so that the cheap reduction of run size is always included, even with outerRetry=0 (in auxiliary function outerseparate) - modified MCAt to set levels to missing rather than that of last row (improves chances for immediate row removal for easy cases) - improved postopNCK to remove rows that have fewer than t non-flexible values - updated CPHFcat and WCS_CAs to updated source status, and updated powerCTcat accordingly

September 23 2025, still version 0.19 - improved N_powerCT by restricting the search to strengths t and t+1 - added a maxN argument to bestCA

September 22 2025, version 0.19 - automated CA_to_MCA in new function MCAt - implemented CPHFs of Wagner, Colbourn and Simos (2022) - reduced powerCTcat to constructions with at most 1000000 runs - implemented fuse for non-prime power v for bestN and bestCA, and removed the preference and override arguments from bestCA in the process - fixed handling of flexible values in productCA and CAEX - improved postopNCK: it now uses a good optimality bound for t>2 as well as for t=2

September 05 2025, version 0.18 - function pcaCA based on the data frame PCAcat: implemented productPCA constructions with promising PCA ingredients (large k1) from Bose (not combining only Bose, because these are in recursiveBose), all cover starter constructions with only one fixed value, and some miscCA designs - function dpCA based on the data frame DPcat: implemented productCA constructions with promising CA ingredients (constant rows) from Bose (not combining only Bose, because these are in recursiveBose), all cover starter constructions with only one fixed value, and some miscCA designs; (basically copied the list from productPCA, more might be achievable with more deliberate array selection) - implemented productPCA constructions with promising PCA ingredients (large k1) from Bose (not combining only Bose, because these are in recursiveBose), all cover starter constructions with only one fixed value, and some miscCA designs - adapted LCDSTCombis with some improved ingredients - adapted power constructions with improved ingredients - apparently nothing changed, but this can not be verified because the old rda file on GitHub appeared to be corrupt - added arguments c1 and c2 for productCA, stopped it from enforcing a PCA (it now instead keeps its constant rows at the top), and changed the default for check to FALSE - included the Cohen simulated annealing CAs and two CAs from Kokkala et al. (2018) into miscCA - included an array from the paper CMMSSY (2006) into miscCA - modified PCAstatus to k in miscCAcat for arrays with v constant rows, and sorted miscCAcat by t, v and k - removed CA_to_PCA from productCA and added it in in CAEX - added new arguments for function productCA with the intention of making it faster - changed SCA_MS to always return an SCA with k1=k-1 - made CMMSSY work as a stand-alone starter construction (always returns SCA with k1=k-1) - added further cover starters from LCDST paper, most to LCDST and the shorter ones to CMMSSY - copied suitable f=1 length k cover starters of LCDST to CMMSSY, where they work for k+1 - improved documentation for CS construction data - bug fix: productPCA did not work for PCAs for which the top right part had level>=i in row i - bug fix: CA_to_PCA removed the attributes from D for the cheap variant without tryhard=TRUE

August 30 2025, version 0.17 - updated the data frame powerCTcat with 179 additional constructions, based on new implementations in the recent past; also, one bug with a claim of a too small design was fixed; several runs are needed, as now some ingredients are of type powerCT - fixed the creation file for powerCTcat in extdata - added nconst columns to ColbournKeriCombis and PALEYcat, and removed redundant rows from ColbournKeriCombis - bug fix: CS_CK did not yield class ca with attributes

August 27 2025, version 0.16 - renamed smcCA to scphfCA, and made its workhorse function internal; adapted everything to that change - modified the workhorse function SMC to avoid the creation of unnecessarily large matrices, and to handle both the SCPHFs from the Sherwood et al. paper (type=“2006”) and from Lanus and co-authors (type=“2018”) by taking care of their respective GFs for v=8 and v=9 - added the Lanus SCPHFs for up to v=9, as far as they improve constructions, in the list CL_SCPHFs - provided further internal functions for Galois field calculations, e.g., the determinant, for checking CPHFs - fixed sloppy writing in the documentation of MTVTRouxtypeCA

August 21 2025, version 0.15 - implemented one more column for strength 3 with v=2^s in SCA_Busht, with consequences also for fuse_BushtCA, and fixed the manual for SCA_Busht and SCA_Bose - adapted the N and k functions for SCA_Busht and fuse_BushtCA - implemented the Sherwood, Martirosyan, Colbourn (2006) construction with CPHFs and permutation vectors - created new file auxiliary_GFcalculus.R that holds all Galois field related auxiliary functions (some moved from auxiliary_functions.R), including a somewhat hacky mygf for handling cases that require a different characteristic polynomial than that used in lhs - improved the documentation of the verbose=2 case for function coverage

August 15 2025, version 0.14

• added constructions by Cohen, Colbourn and Ling (2003, 2008) based on ordered designs, in function ODbasedCA, with N_ and k_ functions, and made it available in Ns and ks and thus bestN and bestCA
• added a CA(12,3,8,2) with two constant runs (available as ca12.2.8, or via miscCA(3,8,2))
• adapted the power construction info to the availability of the CA(12,3,8,2) with two constant rows
• removed three arrays from TJ2level_CAs, and adapted corresponding rows of TJcat; added replacement constructions also for arrays that were never provided because of their size, and removed N results for those
• adapted N_TJcat and k_TJcat to yield result that refers to stored arrays and ignore removed better CAs from other constructions; this way, the actual usage of stored arrays is more transparent
• improved and renamed now internal Martirosyan and van Trung (2004) Roux type implementations, and their referencing of actual theorems in the paper; added a an API function MTVTRouxtypeCA that takes t, k, v as inputs, and added the function N_upper_MTVTRouxtypeCA for the size (which can only yield upper bounds because of unforeseeable number of duplicates that can be removed); not included in Ns and thus in bestCA so far (and probably rarely best, if ever)
• moved SCA_Busht further up in Ns, because its arrays yield better results than OAs in miscCA when used in recursive constructions (via bestCA)
• modified miscCA to not make rows constant per default, because this can make large arrays very slow
• renamed internal function OD to OD2 and moved it to auxiliary_ingredients
• bug fix: made bestCA obey to its argument fixNA

August 11, 2025, version 0.13

• adapted projectionBose to also include the case with s=q+1 and c=1
• created a function projBoseMCA for mixed level CAs
• created a function N_upper_MCA
• removed the futile run size warning for CS_LCDST with f>3
• bug fix: N_CS_LCDST allows k smaller than min(k_implemented), where k_implemented is the smallest k for which there is a starter for the given v; CS_LCDST did not work for k < min(k_implemented); fixed by making it work the same way as CS_MS
• bug fix: k_LCDST did not work correctly (too small) for f > 3
• bug fix: CS_LCDST was not accessible by bestCA because of a typo

08 August 2025, version 0.12

• added CS_CMMSSY for direct cover starters; the arrays have the same sizes as CS_MS, but are guaranteed to be SCAs and can therefore be used recursively with function productPCA (similar to recursiveBose, also implemented in function CS_CMMSSY)
• added function fuse_BushtCA and corresponding N and k functions
• added function compositCA and corresponding N and k functions (for automated composition, using work horse function crossCAs)
• modified N_powerCA and k_powerCA to allow t > requested t (will often yield unattractive numbers; may be reverted after gaining experience)
• added attributes to output of SCA_Busht
• bug fix for crossCAs: construction did not have the correct number of repeats, and yielded a wrong result with a warning
• bug fix for powerCA: cases with implemented t larger than requested t yielded an uncaptured error
• bug fix for dwyerCA: did not work for k less than maximum possible number of columns

04 Aug 2025, version 0.11 - implemented an iterative version of function coverage that also allows to abort at the first non-perfect coverage - fixed a bug that was introduced on 31 July that made coverage fail for mixed level CAs

31 July 2025, still version 0.10 - documented clearly that nlevels order does not determine the output column order in MCA2 - hand over objects from the function environment to the parallel cluster in function coverage - Bug fix: Ns_CK_doubling was wrong for v=3, as it did not multiply plus with v-1

23 July 2025, version 0.10 - modified postopNCK to include an outer loop (new arguments outerRetrymax and outermaxnochange, and seed), and deferred the previous inner workings to an internal function - provide detailed iteration information of postopNCK by messages (suppressible), stating the interim run size achieved at the end of each outer loop, supporting informed decision on early interruption of the process - permit interruption of postopNCK with interim result preserved - implemented stop in postopNCK when lower bound on run size is reached - added function MCA2 for creating strength 2 mixed CAs with a generalization of the first method of Sherwood (2008), as stated in Groemping (2025) - made CA_to_MCA interruptable with latest result returned (as the run size reduction may be slow) - implemented the possibility for outerRetry=0 (suppressing optimization) - made CA_to_MCA and MCA2 return objects with meaningful attributes; handling of the information from the ingoing array may benefit from future improvements - bugfix: postopNCK did not fix the top fixedrows rows; now it does - bugfix: CA_to_MCA was not reproducible for a given seed; now it is

13 July 2025, version 0.9 - added function CA_to_MCA for creating mixed level CAs - changed the output of function postopNCK in case the number of rows cannot be reduced - fixed bug in function postopNCK that led to violation of the requested strength in some cases

10 July 2025, version 0.8 - implemented data file powerCTcat in support of power construction according to Colbourn and Torres-Jimenez (2010) - implemented functions powerCA (with type=“CT”), N_powerCT and k_powerCT and incorporated them into Ns, bestN, bestCA - implemented full factorial for k<=t (which sometimes occurs
for ingredients in recursive constructions) - omitted exclude=“CK_doublingCA” for CK_doubling ingredients, which substantially increases the covered strength 3 scenarii (though not always with competitive arrays) - removed seven arrays from TJcat and TJ2level_CAs, as well as from the folder TJ2level in extdata - moved SCA_Bose and SCA_Busht to a common file with dedicated documentation - fixed various bugs in other constructions that showed up in testing the new function powerCA, among them the number of columns for fuseBoseCA, which was always the maximum instead of the requested k

05 July 2025, version 0.7 - implemented a data file miscCAcat, a function miscCA with N_ and k_ functions, and modified Ns and ks to refer to these - modified oa1728.12.6 to PCA structure, and added further cas / oas, as well as retrieval of a few OAs from DoE.base (handled via miscCAcat); (renamed the R code in extdata for single arrays to miscCAs.R) - implemented the three arrays of source “Chateauneuf-Kreher NRB” - rewrote and re-exported k_fuseBose - removed TJcat arrays that can be replaced by other constructions, and adapted TJcat so that they can still all be constructed - bug fix to productPCA: did not work as expected when trying without success to improve a PCA with tryhard=TRUE

02 July 2025, version 0.6

• added a function bestN for use in size calculations for recursive constructions
• added an internet availability check to function bestCA
• modified ckrsCA, nistCA, dwyerCA and tjCA to throw a meaningful error for cases that are not covered
• extended CS_LCDST to cases with f>3 (uses bestCA for a suitable ingredient)
• fixed LCDSTStarters for v=10 and k=27 and for v=11 and k=26, and correspondingly modified LCDSTCombis
• modified LCDSTCombis$N to hold realistic numbers for f>3 based on the currently available minimum size construction (three different columns for N now)
• added a forgotten entry to DWYERcat, and added useful row names
• added folder extdata with all data files that are used by the package and not available from the internet, as well as code for creating the objects in data folder
• deleted function CK_constrD.R, which was not really for construction D but a duplicate of CK_doubling
• added an argument “exclude” to functions Ns and bestN, in support of recursive constructions that need best sizes for ingredients
• immediately return Bose CA for small k with CAEX, as lineage for N=9 does not exist
• automated CK_doubling via CK_doublingCA with arguments k and v, added an N-function for it and included it in Ns and bestCA
• bug fix for documentation of DHHF

30 June 2025, version 0.5

• bug fix: prevented nonsensical result from N_BoseCA
• bug fix: fixed mistake in N_fuseBose and N_fuseBose_forNs
• bug fix: fixed mistake in LCDSTCombis (for cases with NAs, f was one too large, resulting in too small N; occurred for 7 rows; led to erroneous N reported, but arrays were correct)
• bug fix: fixed mistake in LCDSTStarters for v=7 with k=14
• bug fix: CS_LCDST erroneously refused creation of an array in case of f=3 with NA-values in the starter
• added function fuseBoseCA, in line with the other constructions
• renamed N_fuseBose_forNs to N_fuseBoseCA, in line with the other constructions
• bug fix: hid k_fuseBose, because fixing it takes more care (and it is not so urgently needed)

27 June 2025, version 0.4

• the user-visible data are now in a data folder instead of sysdata.rda, and are documented in more detail
• the Colbourn and Keri (2009) construction was implemented in function CS_CK, and also added to the repertoire for bestCA
• added fuseBose and SCA_Bose to Ns and bestCA
• increased the version number

24 June 2025, Version 0.3

• implemented function bestCA for obtaining the best CA from the currently implemented constructions, based on function Ns
• implemented functions ckrsCA, dwyerCA, nistCA and tjCA for creating designs from catalogues
• added an internal utility function labelToCode that created the suitable code line for function bestCA
• fixed a bug in Ns that led to a deep recursion
• adapted the print method for class ca to new attributes
• added an argument skiplines to readCA

22 June 2025, still Version 0.2.2

• renamed PHF2CA to DHF2CA, as a PHF is a special case of a DHF
• added TJ2level_CAs in support of CT constructions
• made TJcat into data.frame with info column on element name for TJ2level_CAs
• implemented DHHF2CA for heterogeneous DHF CT construction
• added oa1728.12.6 (OA of strength 3 with six 12-level columns based on Ji/Ying construction); this may eventually be moved supplemented with other Ji/Ying OAs, and moved to DoE.base

18 June 2025, still Version 0.2.2

• renamed file CK.R to CK_constrD.R, in line with its content and its documentation file
• fixed a bug in projectionBose (two many rows were made constant)
• fixed a bug in cyclotomyCA (it always returned the maximum number of columns instead of the requested k columns)
• improved PHF2CA to better take advantage of constant rows, in the sense of corollary 2.4 of Colbourn and Torres-Jimenez 2010

05 June 2025, still Version 0.2.2

• renamed previous function projectionBose to fuseBose, as it does a specific type of fusing in line with Colbourn et al. (2010) rather than a projection
• added new function projectionBose that does indeed obtain a projection from a Bose array (Theorem 2.3 of Colbourn 2008; output CA can be uniform or mixed level)
• added new function projBoseCA that allows to input k and v and obtain a projection based uniform CA (uses projectionBose as workhorse function)

25 May 2025, still Version 0.2.2

• added function kd for calculating the k for recursiveBose constructions of type PCA (in some instances based on experimental results), exported this function and function Dd
• made function recursiveBose (and thus recBoseCA) fully exploit the 2PCA structure of the SCA_Bose array
• did the same for function productPCA, if D2=NULL

22 May 2025, Version 0.2.2

• added a function PHF2CA, in support of later implementation of Power constructions
• added a function recBoseCA for creating CAs from recursive processing of several SCA_Bose CAs; that recursive processing was changed from the method by Hartman 2005 (which is still there as recursiveBoseHartman) to using either productPCA (which has the same number of rows but more columns as the Hartman method) or productCA (which has both more rows and more columns), governed by a type argument in functions recBoseCA and recursiveBose
• added further Ns and ks functions for post-processing methods
• changed readCA to take a single path argument including the file name
• added names to the entries of list CKRS_CAs
• bug fix for documentation of productCA and productPCA: run size for D2 was equal to run size for D1, changed it from N to M
• BUG FIX: productCA with generalized=TRUE sometimes failed to make the constant rows distinct, which led to violation of coverage (CAEX was not affected).

19 May 2025, still Version 0.2.1

• added functions Ns and ks
• modified N and k functions, so that most have compatible arguments renamed prior function k_CAEX to k_detail_CAEX
• added names to list entries in WKS_CAs
• added data.frame CYCLOTOMYcat and functions cyclotomyCA, N_CYCLOTOMYcat and k_CYCLOTOMYcat
• augmented the internal object primedat with a few more primes in support of CYCLOTOMYcat

17 May 2025, still Version 0.2.1

• added Paley constructions according to Colbourn (2015)

14 May 2025, still Version 0.2.1

• made function CK_doubling use the CAEX designs per default for 3-level cases (i.e., D2=NULL now works for v=2 and v=3)
• updated function postopNCK from a very naive version to a more serious implementation of the algorithm (which has still not been successful in any challenging case)
• added functions crossSum and directSum
• modified readCA to also read data without separators, where levels 10, 11, … are coded as lower case letters a, b, …
• modified coverage to also work with t=1
• added data.frame CKRScat and list CKRS_CAs
• added several query functions: N_DWYERcat, N_WKScat, N_CKRScat, k_DWYERcat, k_WKScat, k_CKRScat

10 May 2025: Version 0.2.1

• added function CS_LCDST for strength 2 cover starter constructions of Lobb et al. 2012, with internal list LCDSTStarters and internal data.frame object LCDSTCombis with information on what these construct.
• exported function SCA_MS for a rearranged Meagher/Stevens Cover Starter array.
• added function projectionBose to construct array in q^2-3 runs for q+1 factors in q-1 levels (q prime power), according to Colbourn 2008, with corresponding N- and k-functions
• implemented postopNCK to remove rows according to the proposal of Nayeri, Colbourn and Konjevod (2013)
• added internal data.frame DWYERcat with information about the DWYER (2024) CAs database (not yet in any productive use)
• Bug fix: Hartman74 returned fewer than k^2 columns, due to unnecessary removal of constant rows in B

05 May 2025: Version 0.2.0

• renamed function productCA1 to productCA and function productCA2 to crossCAs; separated the documentation file productCA.Rd into three files, corresponding to function names
• the direct product function productCA now also yields the generalized direct product, in the sense that it omits at least 2 and up to v constant rows from the ingoing CAs (after making rows constant, if necessary)
• there are now also functions to calculate k as a consequence of N for the libraries of designs (i.e., eCAK, k_NISTcat, k_TJcat)
• CAEX gained a logical argument maxk1, and the internal object CAEX_lineages gained the information from Torres-Jimenez et al. (2021) about the achievable k1, which is used as the target for k1 maximization.
• various improvements to documentation
• BUG fix: latest state of version 0.1.0 had a serious bug in productPCA and consequently in the PCA-based instances of CAEX, which caused violation of coverage in most situations. This was fixed by using the new internal function productCA_raw within productPCA.

Version 0.1.0: first version on GitHub