Order 816 = 16 + 5*160, from a common submagma at infinity.
C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do.
This magma is C(E, M, 5, B) with
E = magma#6a399a9c87e7071f82c2b558a15c305208ee5447d6f1dcb94d7a1b560bd62e8a,
M = {0, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133, 144, 155, 166} in E,
B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5.
Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B.
TD(5, 160): MacNeish's product over GF(32) x GF(5); GF(32) = F_2[x]/(x^5 + x^2 + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements.
Equation 255: satisfied. Idempotent elements: 51.
qawbecrdtey · 2026-10-07 15:25:48