Date: Sun, 31 Oct 1999 10:38:09 +0200 (EET) From: KOUKOUVINOS CHRISTOS

D-optimal Designs Order 54


m=27, n=54; 2-{27;9,11;7}



A_1={5,6,10,14,16,18,19,21,26}, B_1={5,6,7,8,10,12,13,16,22,25,26}
A_2={5,10,11,15,18,19,22,24,26}, B_2={6,8,11,12,13,14,16,17,23,24,26}
A_3={6,8,11,16,17,19,20,21,26}, B_3={5,9,12,13,15,16,18,20,24,25,26}
A_4={6,8,9,11,16,17,22,23,26}, B_4={5,10,11,13,14,15,17,18,22,24,26}
A_5={6,8,10,12,13,18,22,23,26}, B_5={6,7,12,13,14,15,17,18,21,24,26}
A_6={6,10,14,15,16,18,21,24,26}, B_6={6,9,10,12,17,18,19,22,23,24,26}
A_7={6,9,11,12,13,15,18,23,26}, B_7={6,8,12,13,14,17,18,22,24,25,26}
A_8={6,10,12,13,18,19,21,22,26}, B_8={6,8,9,10,11,14,16,19,20,24,26}
A_9={6,9,10,12,14,18,19,24,26}, B_9={7,8,9,10,12,14,15,18,21,25,26}
A_10={6,7,11,15,17,20,23,24,26}, B_10={7,11,13,14,18,19,21,23,24,25,26}
A_11={7,10,11,13,14,15,20,23,26}, B_11={4,6,11,12,13,17,19,21,22,23,26}
A_12={7,9,16,18,19,21,22,25,26}, B_12={4,7,8,10,12,14,15,20,21,22,26}
A_13={7,10,15,17,20,21,22,24,26}, B_13={5,6,9,10,12,14,15,18,24,25,26}
A_14={7,8,12,17,19,20,23,25,26}, B_14={5,7,9,14,15,16,18,19,21,22,26}
A_15={7,10,12,14,18,19,23,24,26}, B_15={5,6,7,8,10,12,13,16,22,25,26}
A_16={7,9,14,17,18,20,23,24,26}, B_16={6,8,10,11,12,13,17,18,22,25,26}
A_17={7,8,11,13,18,19,20,22,26}, B_17={7,9,10,13,14,16,18,19,23,24,26}
A_18={7,8,9,14,16,19,22,23,26}, B_18={7,9,11,12,16,17,18,20,22,23,26}
A_19={7,9,12,15,16,18,21,22,26}, B_19={7,9,11,14,15,16,21,22,23,25,26}
A_20={8,13,14,15,17,19,23,25,26}, B_20={4,9,11,12,14,18,19,22,23,25,26}
A_21={8,9,14,17,19,22,23,24,26}, B_21={5,9,12,13,15,16,18,20,24,25,26}
A_22={8,9,14,16,17,19,22,23,26}, B_22={5,6,7,9,10,14,16,18,20,21,26}
A_23={8,10,11,16,17,21,23,24,26}, B_23={5,7,9,10,14,15,16,18,19,22,26}
A_24={8,10,12,16,17,20,23,24,26}, B_24={5,6,7,8,11,12,13,16,21,23,26}
A_25={8,9,13,17,18,20,23,24,26}, B_25={5,7,9,10,12,13,17,19,20,21,26}
A_26={8,13,14,15,16,19,22,25,26}, B_26={6,7,9,11,14,15,19,20,22,24,26}
A_27={8,12,13,18,19,21,23,25,26}, B_27={6,8,11,14,15,17,21,22,23,25,26}
A_28={8,9,11,12,15,16,21,24,26}, B_28={6,8,12,14,17,18,19,22,24,25,26}
A_29={8,12,14,17,19,22,23,25,26}, B_29={6,7,11,13,17,18,21,23,24,25,26}
A_30={8,13,14,15,17,20,22,25,26}, B_30={6,7,8,10,12,15,16,20,22,23,26}
A_31={9,10,11,13,14,17,20,22,26}, B_31={4,5,6,7,11,13,16,20,21,24,26}
A_32={9,10,11,15,16,18,19,23,26}, B_32={4,5,6,8,10,12,17,20,22,23,26}
A_33={9,11,13,14,16,17,20,25,26}, B_33={4,6,8,9,10,15,16,18,22,23,26}
A_34={9,12,13,17,19,20,22,24,26}, B_34={4,5,10,12,13,16,21,22,24,25,26}
A_35={9,11,12,14,18,20,21,25,26}, B_35={4,8,9,11,12,14,18,19,20,22,26}
A_36={9,10,11,14,17,18,20,24,26}, B_36={4,6,7,9,11,12,13,18,22,23,26}
A_37={9,10,11,14,16,18,20,23,26}, B_37={5,7,8,12,15,16,20,21,22,23,26}
A_38={9,11,13,16,17,20,23,25,26}, B_38={5,6,11,13,16,20,21,22,24,25,26}
A_39={9,11,13,14,18,19,20,23,26}, B_39={5,8,9,10,12,16,18,21,24,25,26}
A_40={9,11,14,16,17,20,24,25,26}, B_40={5,7,8,9,11,13,14,18,21,25,26}
A_41={9,11,12,17,18,21,22,24,26}, B_41={6,8,9,14,15,17,19,21,22,25,26}
A_42={9,11,14,17,18,20,21,25,26}, B_42={6,7,8,10,14,16,19,20,21,24,26}
A_43={9,12,14,15,18,22,23,24,26}, B_43={6,7,10,12,14,17,18,19,23,24,26}
A_44={9,10,11,15,16,19,23,24,26}, B_44={7,9,10,13,15,16,18,20,22,25,26}
A_45={10,11,13,14,16,19,21,25,26}, B_45={4,5,8,12,15,16,17,18,22,24,26}
A_46={10,12,13,15,16,19,21,25,26}, B_46={5,6,7,11,14,15,19,21,22,24,26}
A_47={11,12,13,15,18,20,22,25,26}, B_47={4,5,7,8,11,15,16,17,21,23,26}
A_48={11,12,14,17,18,21,23,25,26}, B_48={4,5,6,8,10,15,16,18,22,23,26}

Created 1st November 1999 by matrices supplied by Dr Christos Koukouvinos.

Complete searches for D-optimal designs for orders n \leq 54, n=66, were published in:

S.Kounias, C.Koukouvinos, N.Nikolaou, and A.Kakos, The non-equivalent circulant D-optimal designs for n=2mod4, n \leq 54, n=66, J. Combin. Theory Ser. A, 65 (1994), 26-38.