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directed triple system; quasigroup

References:

[1] Brouwer A.E., Schrijver A., Hanani H.: **Group divisible designs with block-size four**. Discrete Math. 20 (1977), 1–10. DOI 10.1016/0012-365X(77)90037-1 | MR 0465894 | Zbl 1093.05008

[2] Colbourn C.J., Hoffman D.G., Rees R.: **A new class of group divisible designs with block size three**. J. Combin. Theory Ser. A 59 (1992), 73–89. DOI 10.1016/0097-3165(92)90099-G | MR 1141323 | Zbl 0759.05012

[3] Drápal A., Kozlik A., Griggs T.S.: **Latin directed triple systems**. Discrete Math. 312 (2012), 597–607. DOI 10.1016/j.disc.2011.04.025 | MR 2854805 | Zbl 1321.05021

[4] Drápal A., Griggs T.S., Kozlik A.R.: **Basics of DTS quasigroups: Algebra, geometry and enumeration**. J. Algebra Appl. 14 (2015), 1550089. MR 3338085 | Zbl 1312.05025

[5] Drápal A., Kozlik A.R., Griggs T.S.: **Flexible Latin directed triple systems**. Utilitas Math.(to appear).

[6] Ge G.: **Group divisible designs**. Handbook of Combinatorial Designs, second edition, ed. C.J. Colbourn and J.H. Dinitz, Chapman and Hall/CRC Press, Boca Raton, FL, 2007, pp. 255–260. MR 2246267

[7] Ge G., Ling A.C.H.: **Group divisible designs with block size four and group type $g^u m^1$ for small $g$**. Discrete Math. 285 (2004), 97–120. DOI 10.1016/j.disc.2004.04.003 | MR 2074843

[8] Ge G., Rees R.S.: **On group-divisible designs with block size four and group-type $6^u m^1$**. Discrete Math. 279 (2004), 247–265. MR 2059993

[9] Ge G., Rees R., Zhu L.: **Group-divisible designs with block size four and group-type $g^u m^1$ with $m$ as large or as small as possible**. J. Combin. Theory Ser. A 98 (2002), 357–376. DOI 10.1006/jcta.2001.3246 | MR 1899631

[10] Hanani H.: **Balanced incomplete block designs and related designs**. Discrete Math. 11 (1975), 255–369. DOI 10.1016/0012-365X(75)90040-0 | MR 0382030 | Zbl 0361.62067

[11] Kozlik A.R.: **Cyclic and rotational Latin hybrid triple systems**. submitted.

[12] McCune W.: **Mace$4$ Reference Manual and Guide**. Tech. Memo ANL/MCS-TM-264, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, August 2003.