Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4) (the unique F_5 linear satisfying eq677). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). Not isomorphic to any F_61-linear magma — those are 82a4911c, d5df0d93, e70931b6, f2d8c865. Same family as the existing Steiner S(2,5,61) magma 03138da9 in the database.
dwrensha · 2026-04-29 23:52:19