MinT - Best Known (139−82, 139, s)-Nets in Base 3

Best Known (139−82, 139, s)-Nets in Base 3

(139−82, 139, 48)-Net over F₃ — Constructive and digital

Digital (57, 139, 48)-net over F₃, using

t-expansion [i] based on digital (45, 139, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(139−82, 139, 64)-Net over F₃ — Digital

Digital (57, 139, 64)-net over F₃, using

t-expansion [i] based on digital (49, 139, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(139−82, 139, 294)-Net in Base 3 — Upper bound on s

There is no (57, 139, 295)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹³⁹, 295, S₃, 82), but
- 5 times code embedding in larger space [i] would yield OA(3¹⁴⁴, 300, S₃, 82), but
  - the linear programming bound shows that MÂ â‰¥ 92990 013044 094514 819920 924216 890382 458823 243090 004189 441252 305046 926521 265386 401339 700505 061242 718668 754527 829137 189654 709670 402661 197008 395913 025082 252699 978005 984047 341957 082104 279920 221352 496075 046560 657058 063672 506100 635927 903287 961024 854326 119081 538084 854071 456687 177310 022577 285742 926380 063698 888663 425324 333440 737727 219825 063034 589750 161818 761953 885200 242213 992264 416023 786479 603085 343734 021730 823670 445661 925152 545016 558250 507360 140052 223149 936574 968153 772241 254682 561735 612867 986901 621147 637493 032183 770505 720964 937818 675474 897354 027643 580600 793369 594905 895283 443173 442804 196955 437013 124039 168938 792674 570654 963503 405910 109582 306492 341297 609348 398671 934529 247156 182573 210469 819835 662365 912246 806321 939172 353408 933277 288233 311953 189149 321408 459707 161191 807654 003277 161211 431932 145709 716553 414678 212172 608231 412557 751553 270075 557611 381189 153574 879516 181260 870101 614449 785056 817502 820712 669073 591462 729526 048000 470716 767568 273850 648446 010405 115639 045880 430501 147523 055575 606013 233614 517597 796603 884471 106121 859005 144552 632075 253203 370381 253897 985465 627273 479040 359147 169210 052419 110525 780505 776382 197073 408770 558107 915008 666940 258873 500630 092550 842979 453860 449891 526523 240794 138486 868445 420130 582062 266303 428577 903004 423801 273506 167989 345975 679222 348628 225026 703554 469121 159312 817260 102976 378712 367374 344192 736810 737884 004685 374730 611865 903893 491487 033759 371650 144343 585871 586306 066457 857585 730076 985125 / 181 251843 461500 692422 259708 200452 540280 444256 897330 362682 739126 645849 883683 070877 798008 059174 338654 437467 514654 012495 224387 670207 907709 834782 758769 933736 414810 101739 944173 594451 607869 488205 881369 839582 433428 935865 282170 610484 584130 004017 263484 850110 944789 699592 485217 034717 439912 696522 318886 900300 713219 405619 937276 016704 672771 090583 329921 052678 061367 817750 406588 532288 871075 892825 527216 737784 757907 625940 261381 658469 725905 455552 121740 670923 154160 819191 910641 515226 969285 508285 592748 236332 923620 038811 063777 216695 679904 345548 155354 052861 399905 234716 954980 920497 222916 729806 140817 164800 843060 572566 943017 778562 535630 856017 598783 678228 822952 836299 034307 409786 447656 479711 085557 277658 589328 135959 057953 870613 251134 924548 356725 789549 089157 088207 491683 572293 120534 255063 024294 109188 804428 597197 237830 285234 617261 999859 922429 745616 123890 284303 351555 127732 864825 260495 148951 601725 418288 413889 847812 437657 245726 418130 752901 201803 170684 420372 099700 709696 110954 399196 501707 788565 796709 220036 314668 840492 497171 956715 242213 090756 128235 480272 705727 920232 001741 737269 094250 418191 746186 011953 998359 062660 217594 258504 607420 595155 263917 989728 518928 539834 075957 722317 845459 922181 760431 168077 815645 451258 572927 227939 176927 347148 129876 595200 881605 913101 705225 754528 173152 645283 289595 717590 017313 229087 497230 287614 286164 869894 448790 526021 765989 836230 937069 980909 > 3¹⁴⁴ [i]

Best Known (139−82, 139, s)-Nets in Base 3

(139−82, 139, 48)-Net over F3 — Constructive and digital

(139−82, 139, 64)-Net over F3 — Digital

(139−82, 139, 294)-Net in Base 3 — Upper bound on s

(139−82, 139, 48)-Net over F₃ — Constructive and digital

(139−82, 139, 64)-Net over F₃ — Digital