MinT - Best Known (116, ∞, s)-Nets in Base 3

Best Known (116, ∞, s)-Nets in Base 3

Digital (116, m, 74)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (116, 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 (116, m, 120)-net over F₃ for arbitrarily large m, using

There is no (116, m, 246)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (116, 1469, 246)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁴⁶⁹, 246, S₃, 6, 1353), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 70 743585 337884 668072 446798 101827 385888 152780 024952 000054 506829 236549 292169 403148 646266 182034 117674 883733 214191 282659 628891 652470 269375 468700 962518 544120 863973 243896 867769 472607 397883 294827 037794 293481 738512 972777 692419 117761 339876 333293 721420 965719 773687 903978 398679 395999 774627 900993 022920 585199 704347 318409 811358 785947 449992 912649 953822 026651 513243 615867 663878 279640 704888 720013 100001 032645 477997 923921 977752 486365 221916 180216 433970 821451 719930 123459 129491 412131 581989 678250 298873 748566 909339 239109 415124 920521 505900 155087 995698 141892 599819 943831 821264 886217 352422 220764 907814 634136 131885 401691 255255 094939 323872 374406 076760 737147 816566 455808 097063 862756 408882 562198 523448 856218 274609 704200 986159 088247 / 677 > 3¹⁴⁶⁹ [i]