The non-existence of symmetric designs for (81, 16, 3) having A_{5} as an automorphism group

Mirjana Garapić, Zagreb, Croatia

Keywords: symmetric design, automorphism group, orbit structure, fixed structure AMS Subject classification: 05B05

Abstract: Some restrictions of the action of prime order subgroups of the alternating group G ≅ A_{5} operating on triplanes for (81, 16, 3) are proved. Then it is shown that G cannot act on a triplane possessing such parameters.