The existence of Schröder designs with equal-sized holes
Holey Schröder designs generalize idempotent Schröder quasigroups. It is shown that when there are \(n\) holes each of size \(h\), a holey Schröder design exists except when \((h, n)\) is \((1, 5)\), \((1, 9)\), \((2, 4)\) or possibly \((6, 4)\), whenever \(h\) is even or \(n\equiv 0, 1\pmod 4\).
scientific article; zbMATH DE number 1047043