MinT - Best Known (113, 113+∞, s)-Nets in Base 3

Best Known (113, 113+∞, s)-Nets in Base 3

Digital (113, m, 74)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (113, 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 (113, m, 120)-net over F₃ for arbitrarily large m, using

There is no (113, m, 240)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (113, 1193, 240)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹¹⁹³, 240, S₃, 5, 1080), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 177 747909 401067 138124 551864 242344 864802 613132 214890 193381 667834 409298 235226 831678 862463 703100 012065 517280 624683 890776 052248 607235 142316 841163 761369 018890 336202 377383 992562 267302 003964 410704 685655 589447 247573 772495 191217 369650 995012 974488 653024 164455 747701 344318 247262 912444 810009 270981 570051 998656 928148 250062 432428 870990 139173 557421 963110 757466 874956 155386 396842 493598 792013 999583 279508 050350 578745 631185 516832 956669 475950 788939 960327 182768 674169 108183 194065 531699 617120 471082 670700 918682 782690 914212 787923 412167 854991 471394 286833 347059 592933 348084 582267 866771 303538 331161 / 1081 > 3¹¹⁹³ [i]