MinT - Best Known (114, ∞, s)-Nets in Base 3

Best Known (114, ∞, s)-Nets in Base 3

Digital (114, m, 74)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (114, 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 (114, m, 120)-net over F₃ for arbitrarily large m, using

There is no (114, m, 242)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (114, 1203, 242)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹²⁰³, 242, S₃, 5, 1089), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 5 205252 149883 255445 415580 853092 841766 060972 955232 358640 395449 928423 688951 272034 244830 298955 004141 137077 431870 117910 996273 682183 140675 111352 736712 600251 900676 481830 170650 287549 893316 729786 583414 470658 353673 504107 448628 600504 811527 445438 743161 120789 461741 520467 638529 595859 627388 296617 671825 447386 912763 933228 407568 471842 186182 208316 461621 815887 620743 548351 090180 295094 922107 704994 674612 779859 953095 816238 441370 663615 942512 280539 049258 202835 233771 558632 647764 300085 050180 261370 037381 750661 668924 732222 718746 011898 138860 429878 504356 394804 405171 466646 616556 084968 810576 103495 286823 / 545 > 3¹²⁰³ [i]