A library of triple arrays and unordered triple arrays

This dataset contains lists of triple arrays and unordered triple arrays generated for the paper "Resolvable Triple Arrays" https://arxiv.org/abs/2512.08681, as well as the source code for the algorithms used to generate this data. Please refer to the paper for all terminology used below. Triple arrays and unordered triple arrays are stored in gzip compressed plain text files. The desription of an (r x c, v)-triple array takes r+1 lines. The first line contains four integers: r, c, v and the autotopism group size. The following r lines each contain c integers from 0 to v-1, the contents of the triple array. Example: 4 9 12 34 6 5 7 10 8 3 11 92 7 6 4 1 0 11 5 103 2 9 1 6 4 0 8 115 8 0 9 3 10 7 1 2 The description of an (r x c, v)-unordered triple array takes r+c+1 lines. The first line contains four integers: r, c, v and the automorphism group size. The following r lines each contain c integers from 0 to v-1, the contents of the row-sets. The last c lines each contain r integers from 0 to v-1, the contents of the column-sets. Example: 3 4 6 242 3 4 50 1 2 50 1 3 41 2 30 2 40 3 51 4 5 Description of the file contents depending on its name: r_c_v_UTA: The complete list of pairwise non-isomorphic (r x c, v)-unordered triple arrays. The arrays are grouped by the corresponding symmetric 2-design in Agrawal's construction, with different groups separated by an empty line. 7_15_35_RUTA: The complete list of pairwise non-isomorphic resolvable (7x15, 35)-unordered triple arrays. The arrays are grouped by the corresponding Kirkman parade in the RUTA construction, with different groups separated by an empty line. r_c_v_RUTA_EX: A list of examples of resolvable (r x c, v)-unordered triple arrays. r_c_v_TA: The complete list of pairwise non-isotopic (r x c, v)-triple arrays. r_c_v_TA_i: The complete list of pairwise non-isotopic (r x c, v)-triple arrays with the underlying unordered triple array which is the i-th in the file r_c_v_UTA (numbering starts from zero). r_c_v_TA_EX: A list of examples of (r x c, v)-triple arrays, with one example corresponding to each unordered triple array in the file r_c_v_UTA. 7_15_35_RTA_i: The complete list of pairwise non-isotopic resolvable (7x15, 35)-triple arrays with the underlying unordered triple array which is the i-th in the file 7_15_35_RUTA (numbering starts from zero). 21_15_63_RTA_EX: A list of examples of resolvable (21x15, 63)-triple arrays, with one example corresponding to each unordered triple array in the file 21_15_63_RUTA_EX. code.tar.gz: The source code for the algorithms used to generate this data, with usage instructions.本数据集包含为论文《Resolvable Triple Arrays》（链接：https://arxiv.org/abs/2512.08681）生成的三元数组与无序三元数组列表，以及用于生成该数据的算法源代码。下文所用全部术语请参阅该论文。 三元数组与无序三元数组均以gzip压缩的纯文本文件存储。 (r×c, v)三元数组的描述占r+1行。首行包含四个整数：r、c、v与自同痕群（autotopism group）大小。后续r行每行各含c个取值范围为0至v-1的整数，即该三元数组的内容。示例如下： 4 9 12 34 6 5 7 10 8 3 11 92 7 6 4 1 0 11 5 103 2 9 1 6 4 0 8 115 8 0 9 3 10 7 1 2 (r×c, v)无序三元数组的描述占r+c+1行。首行包含四个整数：r、c、v与自同构群（automorphism group）大小。后续r行每行各含c个取值范围为0至v-1的整数，即行集内容。最后c行每行各含r个取值范围为0至v-1的整数，即列集内容。示例如下： 3 4 6 242 3 4 50 1 2 50 1 3 41 2 30 2 40 3 51 4 5 根据文件名可区分文件所包含的内容： - `r_c_v_UTA`：全部两两非同构的(r×c, v)无序三元数组列表。数组按阿格拉瓦尔（Agrawal）构造中对应的对称2-设计分组，不同组之间以空行分隔。 - `7_15_35_RUTA`：全部两两非同构的可分解(7×15, 35)无序三元数组列表。数组按RUTA构造中对应的柯克曼游行列分组，不同组之间以空行分隔。 - `r_c_v_RUTA_EX`：可分解(r×c, v)无序三元数组的示例列表。 - `r_c_v_TA`：全部两两非等痕的(r×c, v)三元数组列表。 - `r_c_v_TA_i`：全部两两非等痕的(r×c, v)三元数组列表，其对应的无序三元数组为文件`r_c_v_UTA`中的第i个（编号从0开始）。 - `r_c_v_TA_EX`：(r×c, v)三元数组的示例列表，每个示例对应文件`r_c_v_UTA`中的一个无序三元数组。 - `7_15_35_RTA_i`：全部两两非等痕的可分解(7×15, 35)三元数组列表，其对应的无序三元数组为文件`7_15_35_RUTA`中的第i个（编号从0开始）。 - `21_15_63_RTA_EX`：可分解(21×15, 63)三元数组的示例列表，每个示例对应文件`21_15_63_RUTA_EX`中的一个无序三元数组。 - `code.tar.gz`：用于生成该数据的算法源代码，包含使用说明。