Below are two renditions, entirely equivalent, of the Cayley table for the quasigroup derived from the Steiner system S (3, 4, 8) of section 18B.

listed in full 512 entries

condensed through commutativity 120 entries

aaa=a aab=b aac=c aad=d aae=e aaf=f aag=g aah=h aba=b abb=a abc=d abd=c abe=f abf=e abg=h abh=g aca=c acb=d acc=a acd=b ace=g acf=h acg=e ach=f ada=d adb=c adc=b add=a ade=h adf=g adg=f adh=e aea=e aeb=f aec=g aed=h aee=a aef=b aeg=c aeh=d afa=f afb=e afc=h afd=g afe=b aff=a afg=d afh=c aga=g agb=h agc=e agd=f age=c agf=d agg=a agh=b aha=h ahb=g ahc=f ahd=e ahe=d ahf=c ahg=b ahh=a baa=b bab=a bac=d bad=c bae=f baf=e bag=h bah=g bba=a bbb=b bbc=c bbd=d bbe=e bbf=f bbg=g bbh=h bca=d bcb=c bcc=b bcd=a bce=h bcf=g bcg=f bch=e bda=c bdb=d bdc=a bdd=b bde=g bdf=h bdg=e bdh=f bea=f beb=e bec=h bed=g bee=b bef=a beg=d beh=c bfa=e bfb=f bfc=g bfd=h bfe=a bff=b bfg=c bfh=d bga=h bgb=g bgc=f bgd=e bge=d bgf=c bgg=b bgh=a bha=g bhb=h bhc=e bhd=f bhe=c bhf=d bhg=a bhh=b caa=c cab=d cac=a cad=b cae=g caf=h cag=e cah=f cba=d cbb=c cbc=b cbd=a cbe=h cbf=g cbg=f cbh=e cca=a ccb=b ccc=c ccd=d cce=e ccf=f ccg=g cch=h cda=b cdb=a cdc=d cdd=c cde=f cdf=e cdg=h cdh=g cea=g ceb=h cec=e ced=f cee=c cef=d ceg=a ceh=b cfa=h cfb=g cfc=f cfd=e cfe=d cff=c cfg=b cfh=a cga=e cgb=f cgc=g cgd=h cge=a cgf=b cgg=c cgh=d cha=f chb=e chc=h chd=g che=b chf=a chg=d chh=c daa=d dab=c dac=b dad=a dae=h daf=g dag=f dah=e dba=c dbb=d dbc=a dbd=b dbe=g dbf=h dbg=e dbh=f dca=b dcb=a dcc=d dcd=c dce=f dcf=e dcg=h dch=g dda=a ddb=b ddc=c ddd=d dde=e ddf=f ddg=g ddh=h dea=h deb=g dec=f ded=e dee=d def=c deg=b deh=a dfa=g dfb=h dfc=e dfd=f dfe=c dff=d dfg=a dfh=b dga=f dgb=e dgc=h dgd=g dge=b dgf=a dgg=d dgh=c dha=e dhb=f dhc=g dhd=h dhe=a dhf=b dhg=c dhh=d eaa=e eab=f eac=g ead=h eae=a eaf=b eag=c eah=d eba=f ebb=e ebc=h ebd=g ebe=b ebf=a ebg=d ebh=c eca=g ecb=h ecc=e ecd=f ece=c ecf=d ecg=a ech=b eda=h edb=g edc=f edd=e ede=d edf=c edg=b edh=a eea=a eeb=b eec=c eed=d eee=e eef=f eeg=g eeh=h efa=b efb=a efc=d efd=c efe=f eff=e efg=h efh=g ega=c egb=d egc=a egd=b ege=g egf=h egg=e egh=f eha=d ehb=c ehc=b ehd=a ehe=h ehf=g ehg=f ehh=e faa=f fab=e fac=h fad=g fae=b faf=a fag=d fah=c fba=e fbb=f fbc=g fbd=h fbe=a fbf=b fbg=c fbh=d fca=h fcb=g fcc=f fcd=e fce=d fcf=c fcg=b fch=a fda=g fdb=h fdc=e fdd=f fde=c fdf=d fdg=a fdh=b fea=b feb=a fec=d fed=c fee=f fef=e feg=h feh=g ffa=a ffb=b ffc=c ffd=d ffe=e fff=f ffg=g ffh=h fga=d fgb=c fgc=b fgd=a fge=h fgf=g fgg=f fgh=e fha=c fhb=d fhc=a fhd=b fhe=g fhf=h fhg=e fhh=f gaa=g gab=h gac=e gad=f gae=c gaf=d gag=a gah=b gba=h gbb=g gbc=f gbd=e gbe=d gbf=c gbg=b gbh=a gca=e gcb=f gcc=g gcd=h gce=a gcf=b gcg=c gch=d gda=f gdb=e gdc=h gdd=g gde=b gdf=a gdg=d gdh=c gea=c geb=d gec=a ged=b gee=g gef=h geg=e geh=f gfa=d gfb=c gfc=b gfd=a gfe=h gff=g gfg=f gfh=e gga=a ggb=b ggc=c ggd=d gge=e ggf=f ggg=g ggh=h gha=b ghb=a ghc=d ghd=c ghe=f ghf=e ghg=h ghh=g haa=h hab=g hac=f had=e hae=d haf=c hag=b hah=a hba=g hbb=h hbc=e hbd=f hbe=c hbf=d hbg=a hbh=b hca=f hcb=e hcc=h hcd=g hce=b hcf=a hcg=d hch=c hda=e hdb=f hdc=g hdd=h hde=a hdf=b hdg=c hdh=d hea=d heb=c hec=b hed=a hee=h hef=g heg=f heh=e hfa=c hfb=d hfc=a hfd=b hfe=g hff=h hfg=e hfh=f hga=b hgb=a hgc=d hgd=c hge=f hgf=e hgg=h hgh=g hha=a hhb=b hhc=c hhd=d hhe=e hhf=f hhg=g hhh=h

aaa=a aab=b aac=c aad=d aae=e aaf=f aag=g aah=h abb=a abc=d abd=c abe=f abf=e abg=h abh=g acc=a acd=b ace=g acf=h acg=e ach=f add=a ade=h adf=g adg=f adh=e aee=a aef=b aeg=c aeh=d aff=a afg=d afh=c agg=a agh=b ahh=a bbb=b bbc=c bbd=d bbe=e bbf=f bbg=g bbh=h bcc=b bcd=a bce=h bcf=g bcg=f bch=e bdd=b bde=g bdf=h bdg=e bdh=f bee=b bef=a beg=d beh=c bff=b bfg=c bfh=d bgg=b bgh=a bhh=b ccc=c ccd=d cce=e ccf=f ccg=g cch=h cdd=c cde=f cdf=e cdg=h cdh=g cee=c cef=d ceg=a ceh=b cff=c cfg=b cfh=a cgg=c cgh=d chh=c ddd=d dde=e ddf=f ddg=g ddh=h dee=d def=c deg=b deh=a dff=d dfg=a dfh=b dgg=d dgh=c dhh=d eee=e eef=f eeg=g eeh=h eff=e efg=h efh=g egg=e egh=f ehh=e fff=f ffg=g ffh=h fgg=f fgh=e fhh=f ggg=g ggh=h ghh=g hhh=h