Year: 2025
Type: article
Abstract: A sequence covering array, denoted by ( N ; t , v ), is a set of N permutations of $$\{0, \dots , v-1 \}$$ { 0 , ⋯ , v - 1 } such that each sequence of t distinct elements of $$\{0, \dots , v-1\}$$ { 0 , ⋯ , v - 1 } is a (not necessarily contiguous) subsequence of at least one permutation. The minimum number of permutations such a sequence covering array can have is t ! and it has been conjectured that for $$t > 4$$ t > 4 , if a sequence covering array with t ! permutations exists, then $$v \in \{t,t+1\}$$ v ∈ { t , t + 1 } . In this paper, we prove that an (7!; 7, 10) does not exist. We do this by analysing connections between sequence covering arrays and a special kind of covering array called an excess coverage array.
Source: Designs Codes and Cryptography
Institution: Monash University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4413852205