MinT - Best Known (111, 111+∞, s)-Nets in Base 3

Best Known (111, 111+∞, s)-Nets in Base 3

Digital (111, m, 74)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (111, 73)-sequence over F₃, using
- t-expansion [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

Digital (111, m, 104)-net over F₃ for arbitrarily large m, using

There is no (111, m, 236)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (111, 1173, 236)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹¹⁷³, 236, S₃, 5, 1062), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 51806 506665 058233 233408 853011 009644 515945 275718 587112 940405 614437 598738 685525 957564 220470 824092 460081 527241 717963 274974 220110 073930 218411 074007 512119 745044 029839 406036 919588 281181 664750 336143 205009 455087 463382 016073 438932 391628 126410 522422 287517 299425 410625 738240 825176 548134 882228 689025 907869 945630 494482 181965 813592 203005 443947 379529 428893 894374 276821 428338 124856 504657 998289 582019 898664 246696 167152 494502 497255 973077 773702 542525 804832 417271 547261 270109 220607 176144 583759 905810 957227 969011 874432 990017 535155 572285 073039 997936 511053 566173 936953 447204 865331 913375 / 1063 > 3¹¹⁷³ [i]