MinT - Best Known (180−106, 180, s)-Nets in Base 3

Best Known (180−106, 180, s)-Nets in Base 3

Digital (74, 180, 49)-net over F₃, using

net from sequence [i] based on digital (74, 48)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 48)-sequence over F₉, using
  - s-reduction based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

Digital (74, 180, 84)-net over F₃, using

There is no (74, 180, 299)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁸⁰, 299, S₃, 106), but
- 1 times code embedding in larger space [i] would yield OA(3¹⁸¹, 300, S₃, 106), but
  - the linear programming bound shows that MÂ â‰¥ 324 732527 507624 508238 276452 443811 380138 903465 944216 663896 406405 688104 916728 534542 604995 071253 291225 631601 023419 885880 846290 617872 312295 906173 924218 195526 462181 331954 547642 240463 417212 629164 392071 813044 997896 478399 416251 330679 927819 058957 048870 534936 305325 767878 215607 697812 567955 059860 772745 625888 034156 168427 862600 532511 751369 262621 201250 971317 332055 825335 692059 243516 727295 225005 682413 369223 552235 535905 425238 115354 549450 680568 206963 225671 634741 835847 617006 814376 180939 576777 125847 624110 435589 314283 / 800074 572077 800357 576442 424462 913658 207333 399086 499858 797694 221178 429096 954238 102808 661259 636432 172207 696018 385093 808812 995554 679283 671646 064821 696488 913882 112044 515898 776242 057174 816902 064206 721057 821815 216099 452654 326267 867044 674844 618419 028293 837542 537092 845852 302048 405624 749654 858482 936589 609262 266745 599992 689226 745663 225351 293845 977879 865095 476741 532299 494720 700245 021357 149765 447115 474295 863489 534088 818500 > 3¹⁸¹ [i]